SECOND AMENDED AND RESTATED CERTIFICATE OF DESIGNATION OF

Exhibit 10.3

SECOND AMENDED AND RESTATED

CERTIFICATE OF DESIGNATION OF

THE POWERS, PREFERENCES AND RELATIVE, PARTICIPATING,

OPTIONAL AND OTHER SPECIAL RIGHTS OF PREFERRED UNITS AND

QUALIFICATIONS, LIMITATIONS AND RESTRICTIONS THEREOF

of

12% CUMULATIVE CONVERTIBLE PREFERRED UNITS

for

ATLAS PIPELINE PARTNERS, L.P

ATLAS PIPELINE PARTNERS, L.P., a Delaware limited partnership (the “Company”) pursuant to the provisions of the Delaware Revised Uniform Limited Partnership Act and its Limited Partnership Agreement, does hereby state and certify that pursuant to the authority expressly vested in ATLAS PIPELINE PARTNERS GP, LLC, its general partner (the “General Partner”), the General Partner duly adopted the following resolutions, which remain in full force and effect as of the date hereof:

RESOLVED, that the Amended and Restated Certificate of Designations of the 6.5% Cumulative Convertible Preferred Units, dated as of April 18, 2007, which amended the Certificate of Designations of the 6.5% Cumulative Convertible Preferred Units dated as of March 13, 2006, be and it hereby is amended and restated as follows:

RESOLVED, that each of the 12% Cumulative Convertible Preferred Units rank equally in all respects and shall be subject to the following terms and provisions:

1. Designation. There is hereby created a series of units designated as the “12% Cumulative Convertible Preferred Units.” The number of units (the “Preferred Units”) shall be 40,000 and the face value of each Preferred Unit shall be $1,000 (the “Face Value”). On December 29, 2008, the Company redeemed 10,000 Preferred Units. Pursuant to the Purchase Agreement dated as of January 27, 2009 between the Company and the Holder, the Company shall redeem 10,000 Preferred Units.

2. Definitions. For purposes of this Certificate of Designations, the following terms shall have meanings ascribed to them below:

“Acquisition” means (i) the acquisition by the Company of, or the consummation by the Company of a tender offer for, all of the then outstanding common units of an Affiliated Entity, (ii) the acquisition by an Affiliated Entity of, or the consummation by an Affiliated Entity

of a tender offer for, all of the then outstanding common units of the Company or (iii) the consolidation of the Company and any Affiliated Entity.

“Affiliated Entity” means any corporation, limited partnership, limited liability company, joint venture or other unincorporated organization which is an “affiliate” (as defined in Rule 405 of the Securities Act) of the Company.

“Affiliated Entity Appreciation” shall mean the percentage amount increase in (i) the VWAP of a unit of common equity of the Affiliated Entity that is the subject of the Acquisition on the Trading Day immediately prior to an Announcement and (ii) the average VWAP of a unit of common equity of such Affiliated Entity commencing on the date of the Announcement and ending on the earlier to occur of (A) 60 days thereafter and (B) consummation of the Acquisition.

“Announcement” means the public announcement by the Company of the approval by the General Partner of a merger agreement or tender offering, or of an agreement in principle that includes pricing and/or exchange ratio information, with respect to the Acquisition.

“APL Appreciation” shall mean the percentage amount increase in (i) the VWAP of a Common Unit on the Trading Day immediately prior to an Announcement and (ii) the average VWAP of a Common Unit commencing on the date of the Announcement and ending on the earlier to occur of (A) 60 days thereafter and (B) consummation of the Acquisition.

“Call Option Conditions” means (i) the Company is in compliance with the terms of the Purchase Agreement, this Certificate of Designations and the Registration Rights Agreement; (ii) either the Registrable Securities (as defined in the Registration Rights Agreement) are (A) eligible for resale without restriction pursuant to Rule 144(b) under the Securities Act of 1933, as amended (the “Securities Act”) or (B) are covered by an effective registration statement (the “Registration Statement”) and such registration statement is not subject to any suspension or stop orders, the prospectus contained therein is current and deliverable and not subject to any blackout or similar circumstance; (iii) the Registrable Securities (as defined in the Registration Rights Agreement (as defined below)) are listed on the Principal Market; and (iv) the Company is not subject to any bankruptcy, insolvency or similar proceeding.

“Change of Control” means the occurrence of any of the following:

(1) the direct or indirect sale, lease, transfer, conveyance or other disposition (other than by way of merger or consolidation), in one or a series of related transactions, of all or substantially all of the properties or assets of the Company and its subsidiaries taken as a whole, to any “person” (as that term is used in Section 13(d)(3) of the Exchange Act);

(2) the adoption of a plan relating to the liquidation or dissolution of the Company or the removal of the General Partner by the limited partners of the Company;

(3) the consummation of any transaction (including, without limitation, any merger or consolidation) the result of which is that any “person” or “group” (as those terms are

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used in Section 13(d)(3) or Section 14(d)(2) of the Exchange Act, or any successor provision), becomes the beneficial owner, directly or indirectly, of more than 50% of the Voting Stock of the General Partner, measured by voting power rather than number of shares; provided that a change of control shall not be deemed to occur solely as a result of a transfer of the general partnership interests of the Company or the equity interests in the General Partner to a new entity in contemplation of the initial public offering of such new entity, or as a result of any further offering of equity interests of such new entity (or securities convertible into such equity interests) so long as the persons or entities that beneficially own the general partnership interests of the Company or the equity interests in the General Partner on the Closing Date continue to hold the general partnership interests in such new entity (or, in the case of a new entity that is not a partnership, no other person or group beneficially owns more than 50% of the Voting Stock of such new entity);

(4) the Company consolidates or merges with or into another person or any person consolidates or merges with or into the Company, in either case under this clause (4) in one transaction or a series of related transactions in which immediately after the consummation thereof persons beneficially owning, directly or indirectly, Voting Stock representing in the aggregate a majority of the total voting power of the Voting Stock of the Company immediately prior to such consummation do not beneficially own, directly or indirectly, Voting Stock representing a majority of the total voting power of the Voting Stock of the Company or the surviving or transferee person; or

(5) the first day on which a majority of the members of the Board of Directors of the General Partner are not Continuing Directors.

“Closing Price” shall mean $22.00, as such Closing Price may be adjusted pursuant to Section 6(d) of this Certificate of Designation.

“Common Units” shall mean the common units representing limited partner interests of the Company.

“Continuing Directors” means, as of any date of determination, any member of the Board of Directors of the General Partner who (1) was a member of such Board of Directors on the Closing Date or (2) was nominated for election or elected to such Board of Directors with the approval of either (x) a majority of the Continuing Directors who were members of such Board at the time of such nomination or election, or (y) any “person” or “group” (as those terms are used in Section 13(d)(3) or Section 14(d)(2) of the Exchange Act, or any successor provision) who owns all the general partnership interests or a majority of the equity interests of the General Partner.

“Conversion Commencement Date” shall mean April 1, 2009.

“Conversion Price” shall mean the lesser of (a) the Closing Price or (b) 95% of the Market Price as of the Conversion Notice Date (as defined below); provided, however, if the Company elects to pay the Conversion Value to Holder instead of issuing Common Units, the Conversion Price shall be the lesser of (a) the Closing Price or (b) 100% of the Market Price as of the Conversion Notice Date.

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“Conversion Value” shall mean: (i) if the Closing Price is less than the Market Price, the number of Common Units issuable for the Preferred Units being converted or redeemed multiplied by the Market Price and (ii) if the Closing Price is greater than or equal to the Market Price, the Liquidation Value (as defined below) of the Preferred Units being converted or redeemed.

“Currency Conversion Option” shall mean the right of the Company to satisfy a Conversion Notice by paying to the Holder the Conversion Value as of the Conversion Notice Date or Mandatory Conversion Date, as appropriate, rather than issuing Common Units to it.

“Dividend Commencement Date” shall mean March 13, 2008.

“Exchange Act” shall mean the Securities Exchange Act of 1934, as amended.

“First Call Date” shall mean May 9, 2007.

“First Call Redemption Price” equals $51.17 per unit (as may be adjusted pursuant to Section 6(d)).

“Holder” means Sunlight Capital Partners, LLC or any of its transferees permitted pursuant to the terms of the Purchase Agreement (as defined below).

“Mandatory Conversion Date” shall mean the second year anniversary of the Conversion Commencement Date, provided however, that if the Call Option Conditions shall not have been satisfied for the 20 Trading Days immediately preceding such date, the Mandatory Conversion Date shall be such later date as such conditions shall have been satisfied.

“Market Price” shall mean the average closing price of a Common Unit over the ten (10) consecutive Trading Days immediately preceding the date as of which the Market Price is being determined, provided that if the Common Units are not then listed on any market or exchange, then the Market Price shall be the average of the closing bid prices for the Common Units on the OTC Bulletin Board, or, if such is not available, the National Quotation Bureau, or otherwise the average of the closing bid prices for the Common Units quoted by two market-makers of the Common Unit, or otherwise such Market Price shall be the fair market value of one Common Unit as reasonably determined in good faith by the Company and the Holders of a majority of the Preferred Units.

“Principal Market” shall mean the New York Stock Exchange or such other principal market or exchange on which the Common Units are then listed for trading.

“Redemption Date” shall mean the date upon which a redemption effected pursuant to the exercise of a Call Option or Special Call Option shall be consummated.

“Second Call Date” shall mean November 9, 2007.

“Second Call Redemption Price” shall mean $27.25 per unit (as such price may be adjusted pursuant to Section 6(d)).

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“Senior Notes Restrictions” shall mean Section 4.08 of the Indenture, dated as of December 20, 2005, by and among the Company, its subsidiaries named therein and Wachovia Bank, National Association relating to the Company’s 8- ¹/8% Senior Notes due 2015, and Section 4.08 of the Indenture, dated as of June 27, 2008, by and among the Company, its subsidiaries named therein and U.S. Bank National Association relating to the Company’s 8- ³/4% Senior Notes due 2018.

“Special Call Redemption Price” shall mean the following based upon the date on which the Special Call Option is exercised:

“Trading Day” shall mean a day on which there is trading on the New York Stock Exchange or such other market or exchange on which the applicable security is then principally traded.

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“Voting Stock” of any person as of any date means the equity interests of such person pursuant to which the holders thereof have the general voting power under ordinary circumstances to elect at least a majority of the board of directors, managers, general partners or trustees of such person (regardless of whether, at the time, equity interests of any other class or classes shall have, or might have, voting power by reason of the occurrence of any contingency) or, with respect to a partnership (whether general or limited), any general partner interest in such partnership.

“VWAP” means, for any security as of any date, the summary volume-weighted average price, rounded to four decimal places, for such security on all reported exchanges during the period beginning at 9:30 a.m., New York City Time, and ending at the closing of such exchange, at or about 4:00 p.m., New York City Time, as reported by Bloomberg, L.P. (or any successor thereto, “Bloomberg”) through its “Volume at Price” functions, or, if no dollar volume-weighted average price is reported for such security by Bloomberg for such hours, the average of the highest closing bid price and the lowest closing ask price of any of the market makers for such security as reported in OTC Bulletin Board or, if unavailable, as reported in the “pink sheets” by the National Quotation Bureau, Inc.

3. Dividends. Commencing on the Dividend Commencement Date and until December 31, 2008, the Holders of the Preferred Units shall be entitled to receive cumulative dividends at the per unit rate of six and a half percent (6.5%) per annum of the Face Value of each outstanding Preferred Unit. Commencing on January 1, 2009, the Holders of the Preferred Units shall be entitled to receive cumulative dividends at the per unit rate of twelve percent (12%) per annum of the Face Value of each outstanding Preferred Unit. Dividends shall be paid on the same date (a “Dividend Payment Date”) as the dividend payment date for Common Units and the record dates for dividends on the Preferred Units and Common Units shall be the same. Dividends shall accrue on each Dividend Payment Date. Payment of dividends on the Preferred Units shall be in preference and priority to any payment of any dividend or other distribution on the Common Units or any other class or series of equity security of the Company, including, without limitation, any series of units or Incentive Distribution Rights, other than the Company’s 12% Cumulative Convertible Class B Preferred Units (the “Class B Preferred Units”), with which dividend payments shall be pari passu. If at any time dividends on the outstanding Preferred Units at the rate set forth above shall not have been paid or declared and set apart for payment with respect to all preceding periods, the amount of the deficiency shall be fully paid or declared and set apart for payment before any distribution, whether by way of dividend or otherwise, shall be declared or paid upon or set apart for the Common Units or any other class or series of equity security, including, without limitation, any series of units or Incentive Distribution Rights, of the Company, other than the Class B Preferred Units. Notwithstanding anything in this Section 3 to the contrary, with respect to Preferred Units which are converted with Common Units, the Holder shall not be entitled to a Preferred Unit dividend and a Common Unit dividend with respect to the same period, but shall be entitled only to the dividend to be paid based upon the class of equity held on the record date. Thus, if Holder converts Preferred Units into Common Units prior to a record date, on the applicable Dividend Payment Date, it shall receive the Common Unit dividend with respect to such units and if the Holder converts Preferred Units after a record date, on the applicable Dividend Payment Date, it shall receive the Preferred Unit dividend.

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4. Liquidation Value. In the event of any liquidation, dissolution or winding up of the Company, either voluntary or involuntary, the Holders of the Preferred Units shall be entitled to receive, out of the assets of the Company available for distribution to unit holders, prior and in preference to any distribution of any assets of the Company to the holders of any other class or series of equity securities, other than the Class B Preferred Units, the amount of Face Value per unit plus all accrued but unpaid dividends thereon and all liquidated damages payable under the Registration Rights Agreement (as defined below) which have not yet been paid (collectively, the “Liquidation Value”). The foregoing shall not affect any rights which Holders of Preferred Units may have with respect to any requirement that the Company repurchase the Preferred Units or for any right to monetary damages.

5. Issuance of Preferred Units. The Preferred Units shall be issued by the Company pursuant to a Purchase Agreement, dated as of March 13, 2006 (the “Purchase Agreement”) between the Company and the initial subscriber for the Preferred Units thereunder (collectively, the “Subscriber”), and Holders of Preferred Units shall enjoy the benefits of the Registration Rights Agreement, dated as of March 13, 2006 (the “Registration Rights Agreement”) between such parties in connection with the Purchase Agreement to the extent set forth therein.

6. Conversion.

a) Conversion at Option of Holders. Commencing on the Conversion Commencement Date, subject to the terms hereof, each Holder of the Preferred Units shall have the right at any time and from time to time, at the option of such Holder, to request conversion of any or all Preferred Units held by such Holder for such number of fully paid, validly issued and nonassessable Common Units, free and clear of any liens, claims or encumbrances, as is determined by dividing (i) the Liquidation Value times the number of Preferred Units being converted, by (ii) the applicable Conversion Price on the Conversion Notice Date (subject to the limitations set forth in this Section 6). Immediately following such conversion, the rights of the Holders of converted Preferred Units, including without limitation, any accrual of dividends, shall cease and the persons entitled to receive the Common Units upon the conversion of Preferred Units shall be treated for all purposes as having become the owners of such Common Units.

b) Mandatory Conversion. On the Mandatory Conversion Date, all then outstanding Preferred Units shall be automatically converted into Common Units, determined in the manner set forth in paragraph (a) above; provided however, that the applicable Conversion Price shall be the Conversion Price based on the ten Trading Days immediately preceding the Mandatory Conversion Date; provided, however, that in lieu of converting the Preferred Units, the Company may exercise the Currency Conversion Option, provided that has provided the Holder with written notice of such exercise no later than 10 Trading Days prior to the Mandatory Conversion Date.

c) Mechanics of Conversion. To convert Preferred Units into Common Units, the Holder shall give written notice (“Conversion Notice”) to the Company in the form of page 1 of Exhibit A hereto (which Conversion Notice may be given by facsimile transmission) stating that such Holder elects to convert the same and shall state therein the number of Preferred

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Units to be converted; provided that such number must be at least the lesser of 10,000 or the number of outstanding Preferred Units, and the name or names in which such Holder wishes the certificate or certificates for Common Units to be issued. The date of the Conversion Notice shall be hereinafter be referred to as the “Conversion Notice Date.” The Holder may not submit more than one Conversion Notice during any 30 day period. No later than 5 Trading Days after receipt of the Conversion Notice, the Company shall notify Holder in writing (the “Company Notice”) of its option to either (i) issue Common Units to Holder or (ii) pay to Holder the Conversion Value of the Preferred Units in cash pursuant to the Currency Conversion Option. The Company shall then either issue the Common Units or pay the Conversion Value of the Preferred Units being redeemed, as indicated to the Holder, on a date (the “Conversion Date”) no later than 30 days after Conversion Notice Date. In the event that the Company shall have elected to issue Common Units, the Company shall, in the Company Notice, indicate its computation of the number of Common Units to be received by Holder. On the Conversion Date and subject to the book-entry provisions set forth below, such Holder shall surrender the certificate or certificates representing the Preferred Units being converted, duly endorsed, at the office of the Company or, if identified in writing to Holder by the Company, at the offices of any transfer agent for such units. If the Company shall have elected to pay the Conversion Value to Holders on the Conversion Date, it shall wire Federal Funds in the amount of the Conversion Value to the account of the Holder specified by Holder to the Company. If the Company has elected to issue Common Units, then on the Conversion Date, the Company shall issue Holder a certificate or certificates for the number of Common Units to which such Holder shall be entitled (with the number of and denomination of such certificates designated by such Holder), and the Company shall immediately issue and deliver to such Holder a certificate or certificates for the number of Preferred Units (including any fractional shares) which such Holder has not yet elected to convert hereunder but which are evidenced in part by the certificate(s) delivered to the Company in connection with such Conversion Notice. If certificates evidencing the Common Units are not received by the Holder within five (5) Trading Days of the Conversion Date, then the Holder will be entitled to: (i) revoke and withdraw its Conversion Notice, in whole or in part, at any time prior to its receipt of those certificates or (ii) be paid immediately the Conversion Value by the Company instead of receiving Common Units. In lieu of delivering physical certificates representing the Common Units issuable upon conversion of Preferred Units, provided the Company’s transfer agent is participating in the Depository Trust Company (“DTC”) Fast Automated Securities Transfer (“FAST”) program, upon request of the Holder, the Company shall use its best efforts to cause its transfer agent to electronically transmit the Common Units issuable upon conversion or dividend payment to the Holder, by crediting the account of the Holder’s prime broker with DTC through its Deposit Withdrawal Agent Commission (“DWAC”) system. The time periods for delivery described above, shall apply to the electronic transmittals through the DWAC system. The parties agree to coordinate with DTC to accomplish this objective. The conversion pursuant to this Section 6 shall be deemed to have been made immediately prior to the close of business on the Conversion Date. The person or persons entitled to receive the Common Units issuable upon such conversion shall be treated for all purposes as the record Holder or Holders of such Common Units at the close of business on the Conversion Date.

Notwithstanding the foregoing, if an Announcement shall have been made, then (a) the number of Common Units issuable upon conversion of the Preferred Units shall be the number determined pursuant to Section 6(a) above multiplied by a factor (the “Premium

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Factor”) equal to the sum of (x) 100% and (y) the greater of the Affiliated Entity Appreciation and the APL Appreciation and (b) if the Company elects to pay Conversion Value, the Conversion Value shall be adjusted by multiplying it by the Premium Factor.

The Company’s obligation to issue Common Units or pay the Conversion Value upon conversion of Preferred Units shall, subject to compliance with this subsection in all material respects, be absolute, is independent of any covenant of any Holder of Preferred Units, and shall not be subject to: (i) any offset or defense; or (ii) any claims against the Holders of Preferred Units whether pursuant to this Certificate of Designations, the Purchase Agreement, the Registration Rights Agreement, or otherwise.

Book-Entry. Notwithstanding anything to the contrary set forth herein, upon conversion of any Preferred Units in accordance with the terms hereof, the Holder thereof shall not be required to physically surrender such Holder’s certificates for Preferred Units to the Company unless such Holder is converting all of the Preferred Units then held by such Holder. The Holders of Preferred Units and the Company shall maintain records showing the number of Preferred Units so converted hereunder, the number of Common Units received upon conversion and the dates of such conversions, or shall use such other method, reasonably satisfactory to the Holders and the Company, so as not to require physical surrender of certificates for Preferred Units upon each such conversion. Notwithstanding the foregoing, if any Preferred Units are converted as aforesaid, such Holder of Preferred Units may not transfer its Preferred Units unless such Holder first physically surrenders to the Company all certificates representing any Preferred Units which have previously been converted in whole or in part, whereupon the Company will forthwith issue and deliver upon the order of such Holder new certificate(s) evidencing Preferred Units, registered as such Holder may request, representing in the aggregate, together with all other certificates evidencing Preferred Units held by such Holder, the remaining number of Preferred Units held by such Holder. Each Holder of Preferred Units (and any successor in interest or assignee), by acceptance of Preferred Units, acknowledges that, by reason of the provisions of this paragraph, following conversion of any Preferred Units, the number of Preferred Units actually owned by such Holder may be less than the number of Preferred Units set forth on the face of the certificates representing Preferred Units and held by such Holder.

d) Conversion Adjustments.

(i) If the Company or any of its subsidiaries, at any time while the Preferred Units are outstanding (A) shall pay a unit dividend or otherwise make a distribution or distributions on any equity securities (including instruments or securities convertible into or exchangeable for such equity securities) in Common Units, (B) subdivide outstanding Common Units into a larger number of units, or (C) combine outstanding Common Units into a smaller number of units, then each Affected Price (as defined below) shall be multiplied by a fraction, the numerator of which shall be the number of Common Units outstanding before such event and the denominator of which shall be the number of Common Units outstanding after such event. Any adjustment made pursuant to this Section 6(d)(i) shall become effective immediately after the record date for the determination of unit holders entitled to receive such dividend or distribution and shall become

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effective immediately after the effective date in the case of a subdivision or combination.

As used herein, the Affected Prices (each an “Affected Price”) shall refer to: (i) the Closing Price, First Call Redemption Price, Second Call Redemption Price or Low Price (as defined in Section 7(f)); or, as applicable, (ii) each closing price for Common Units occurring on any Trading Day included in the period used for determining the Market Price, which Trading Day occurred before the record date in the case of events referred to in clause (A) of this subparagraph 6(d)(i) and before the effective date in the case of the events referred to in clauses (B) and (C) of this subparagraph 6(d)(i).

(ii) If the Company or any of its subsidiaries, at any time while the Preferred Units are outstanding, shall distribute to all holders of Common Units evidences of its indebtedness or assets or cash (other than the Company’s regularly declared and scheduled dividend) or rights or securities (excluding those referred to in Section 6(d)(i) above and 6(d)(iii) below) or warrants to subscribe for or purchase any security of the Company or any of its subsidiaries (excluding those referred to in Section 6(d)(i) above and 6(d)(iii) below), then each Affected Price shall be adjusted by multiplying the existing Affected Price, by a fraction, (A) the numerator of which is the closing price per Common Unit immediately prior to the record date fixed for determination of Holders of Common Units entitled to receive the distribution (the “Reference Price”) less the fair market value per Common Unit at such record date of the distribution as reasonably determined by the General Partner in good faith and (B) the denominator of which is the Reference Price; provided, however, that if the Holder disputes the General Partner’s valuation above, the Holder and the Company shall select a mutually acceptable appraiser (the “Appraiser”) whose fee shall be borne equally by the Holder and the Company, and the fair market value of such distribution shall be as determined by the Appraiser.

(iii) Prior to the consummation of any recapitalization, reorganization, consolidation, merger, spin-off or other business combination (other than a Change in Control Transaction) pursuant to which holders of Common Units are entitled to receive securities or other assets with respect to or in exchange for Common Units (a “Company Event”), the Company shall make appropriate provision to insure that the Holder will thereafter have the right to receive upon a conversion of its Preferred Units at the Conversion Price in lieu of the Common Units otherwise receivable upon such conversion, such securities or other assets received by the holders of Common Units in connection with the consummation of such Company Event in such amounts as the Holder would have been entitled to receive had the Preferred Units initially been issued with a conversion rights for the form of such consideration (as opposed to Common Units) at a conversion ratio for such consideration equal to a fraction, the numerator of which is the outstanding Liquidation Value multiplied by the number of outstanding Preferred Units and the denominator of which is the Conversion Price. Provision made

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pursuant to the preceding sentence shall be in a form and substance satisfactory to the Holders.

(iv) In case of any Change of Control, then without limiting other rights hereunder, the Holder shall have the right thereafter to, at its option, (A) convert Preferred Units, in whole or in part, at the Conversion Price, into the units and other securities, cash and/or property receivable upon or deemed to be held by holders of Common Units following such Change of Control, and such conversion shall be effected on the closing of the Change of Control (B) subject to the Senior Notes Restrictions, require the Company or its successor to redeem, within five days of notice to the Company, the Preferred Units, in whole or in part, at a redemption price equal to the greater of (x) the Liquidation Value of the Preferred Units or (y) the Conversion Value of the Preferred Units. To the extent that Holder does not exercise its option described in the immediately preceding sentence, the terms of any such Change in Control Transaction shall include such terms so as to continue to give to the Holders the right to receive the amount of securities, cash and/or property upon any conversion or redemption following such Change in Control Transaction to which a holder of the number of Common Units deliverable upon such conversion would have been entitled in such Change in Control Transaction. This provision shall similarly apply to successive reclassifications, consolidations, mergers, sales, transfers or share exchanges. Holder’s right to convert pursuant to clause (A) above shall be irrespective of whether it has previously submitted a Conversion Notice within the prior 30 days.

e) Notice of Record Date. In the event of any taking by the Company of a record date of the holders of any class of securities for the purpose of determining the holders thereof who are entitled to receive any dividend or other distribution, any security or right convertible into or entitling the holder thereof to receive additional Common Units, or any right to subscribe for, purchase or otherwise acquire any shares of stock of any class or any other securities or property, or to receive any other right, the Company shall notify each Holder of Preferred Units at least 15 days prior to the record date, of which any such record is to be taken for the purpose of such dividend, distribution, security or right and the amount and character of such dividend, distribution, security or right; provided, however, that the foregoing requirement shall be deemed satisfied if at least 15 days prior to record date, the Company shall have issued a press release which shall be posted on the Company’s website and carried by one or more wire services, containing the required information.

f) Issue Taxes. The Company shall pay any and all issue, documentary, stamp and other taxes, excluding any income, franchise or similar taxes, that may be payable in respect of any issue or delivery of Common Units on conversion of, or payment of dividends on, Preferred Units pursuant hereto. However, the Holder of any Preferred Units shall pay any tax that is due because the Common Units issuable upon conversion thereof or dividend payment thereon are issued in a name other than such Holder’s name.

g) Other Redemption Rights.

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(i) Redemption Option upon Acquisition. If the Company offers cash as consideration for the Acquisition, then without limiting other rights hereunder, the Holder shall have the right thereafter, subject to the Senior Notes Restrictions, to demand the Company or its successor to redeem, 30 days after the consummation of the Acquisition, the Preferred Units at a redemption price equal to the Conversion Value of such Preferred Units, multiplied by the Premium Factor (the “Acquisition Redemption Amount”). The Company shall not pay cash as consideration for the Acquisition unless it has set aside reserves equal to the Acquisition Redemption Amount. No later than 5 Trading Days after receipt of the Holder’s demand, the Company shall notify Holder in writing of its option to either (i) pay the Acquisition Redemption Amount or (ii) issue such number of Common Units to the Holder as is determined by dividing (A) the Liquidation Value times the number of Preferred Units for which a redemption demand has been made by (B) the lesser of (a) the Closing Price or (b) 90% of the Market Price as of the redemption demand date, and then multiplying by the Premium Factor.

(ii) April 2009 Redemption. The Company shall redeem 10,000 Preferred Units on April 1, 2009 at a redemption price, payable in cash, equal to the Liquidation Value of such Preferred Units.

(iii) July 2009 Redemption. If the Company has not received a Conversion Notice with respect to the last 10,000 outstanding Preferred Units on or before June 2, 2009, on July 1, 2009 the Company shall redeem such Preferred Units by (A) paying to Holder the Liquidation Value of the Preferred Units in cash pursuant to the Currency Conversion Option or (B) paying one-half of the Liquidation Value by issuing Common Units to the Holder and one-half the Liquidation Value in cash.

h) Fractional Units. No fractional Common Units shall be issued upon the conversion of any Preferred Units. All Common Units (including fractions thereof) issuable upon conversion of more than one Preferred Unit by a Holder thereof shall be aggregated for purposes of determining whether the conversion would result in the issuance of any fractional unit. If, after the aforementioned aggregation, the conversion would result in the issuance of a fraction of a Common Unit, the Company shall, in lieu of issuing any fractional unit, either round up the number of units to the next highest whole number or, at the Company’s option, pay the Holder otherwise entitled to such fraction a sum in cash equal to the fair market value of such fraction on the Conversion Date (as determined in good faith by the General Partner of the Company).

i) Specific Enforcement. The Company agrees that irreparable damage would occur in the event that any of the provisions of this Certificate of Designations were not performed in accordance with their specific terms or were otherwise breached. Each Holder shall have all rights and remedies set forth in this Certificate and all rights and remedies which such Holders have been granted at any time under any other agreement or contract and all of the rights which such Holders have under any law. Any person having any rights under any provision of this Certificate shall be entitled to enforce such rights specifically or pursue other

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injunctive relief or other equitable remedies (without posting a bond or other security), to recover damages by reason of any breach of any provision of this Certificate and to exercise all other rights granted by law. Each Holder without prejudice may withdraw, revoke or suspend its pursuit of any remedy at any time prior to its complete recovery as a result of such remedy.

j) Limitations on Issuance of Common Units.

(A) 9.9% Limitation. Notwithstanding anything to the contrary contained herein, the number of Common Units that may be acquired by the Holder upon conversion or redemption of the Preferred Units pursuant to the terms hereof shall not exceed a number that, when added to the total number of Common Units deemed beneficially owned by such Holder (other than by virtue of the ownership of securities or rights to acquire securities (including the Preferred Units) that have limitations on the Holder’s right to convert, exercise or purchase similar to the limitation set forth herein), as determined pursuant to the rules and regulations promulgated under Section 13(d) of the Exchange Act, including all Common Units deemed beneficially owned at such time (other than by virtue of the ownership of securities or rights to acquire securities that have limitations on the right to convert, exercise or purchase similar to the limitation set forth herein) by persons that would be aggregated for purposes of determining whether a group under Section 13(d) of the Exchange Act, exists, would exceed 9.9% of the total issued and outstanding Common Units (the “Restricted Ownership Percentage”). The Holder shall have the right (w) at any time and from time to time to reduce its Restricted Ownership Percentage immediately upon notice to the Company and (x) (subject to waiver) at any time and from time to time, to increase its Restricted Ownership Percentage immediately in the event of the announcement as pending or planned, of a Change in Control Transaction. If the Company elects to issue Common Units to Holder pursuant to the provisions hereof, whether as a result of a conversion or redemption of the Preferred Units, and such issuance would in and of itself exceed the Restricted Ownership Percentage, then with respect to the Common Units that would cause the Restricted Ownership Percentage to be exceeded, the Company shall pay in cash to Holder an amount equal to the Market Price multiplied by the number of excess Common Units (“Excess Amount”).

(B) Principal Market Regulation. The Company shall not be obligated to issue any Common Units upon conversion of the Preferred Units, whether pursuant to this Section 6, or otherwise, if the issuance of such Common Units would exceed that number of units of Common Units which the Company may issue upon conversion of the Preferred Units without breaching the Company’s obligations under the rules or regulations of the Principal Market (the “Principal Market Cap”). To the extent that the Preferred Units are converted for a number of Common Units that would exceed the Principal Market Cap, the Company shall pay in cash to Holder the Excess Amount.

7. Company Redemption Rights.

a) Prior to the First Call Date, the Company shall have the option (the “Special Call Option”), subject to the conditions set forth below, to redeem all, but not less than all, of the Preferred Units for an aggregate cash amount equal to the product of (A) the

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Liquidation Value of the outstanding Preferred Units divided by the Conversion Price; multiplied by (B) the Special Call Redemption Price.

b) The exercise of the Special Call Option by the Company shall be subject to the following conditions: (i) transmission of a written notice (“Special Call Option Notice”) no sooner than 20 Trading Days prior to the Redemption Date, which notice shall specify the Redemption Date; and (ii) if the Redemption Date shall occur after the Conversion Commencement Date, the satisfaction of the Call Option Conditions on the 20 consecutive Trading Days immediately preceding the date of the Special Call Option Notice and at all times from such date to the applicable Redemption Date.

c) The Company shall have the option (the “Call Option”) to (A) on or after the First Call Date but no later than the Second Call Date redeem some or all of the outstanding Preferred Units for cash, for an amount determined by dividing the Liquidation Value of the Preferred Units being redeemed by the Conversion Price and multiplying by the First Call Redemption Price; and (B) on or after the Second Call Date, redeem some or all outstanding Preferred Units for cash, for an amount determined by dividing the Liquidation Value of the Preferred Units being redeemed by the Conversion Price and multiplying by the Second Call Redemption Price; provided, however, that the foregoing redemptions must be exercised for no less than the lesser of: (x) 10,000 Preferred Units, or (y) the number of remaining outstanding Preferred Units. However, the foregoing right shall not affect the right of the Holder to convert Preferred Units pursuant to the terms of Section 6(a) with respect to any Conversion Notice submitted by Holder prior to a Redemption Date and the conversion of such Preferred Units shall be governed by the provisions of Section 6(a) and not this Section 7.

d) The exercise of the Call Option by the Company shall be subject to: (i) the transmission of a written notice of the exercise of the Call Option to the Holder (the “Call Option Notice”) no later than 10 Trading Days prior to the applicable Redemption Date which shall specify the amount of Preferred Units being redeemed; and (ii) the satisfaction of the Call Option Conditions on the 20 Trading Days immediately preceding the Call Option Notice and at all times from the Call Option Notice to the applicable Redemption Date.

e) With respect to exercises of the Special Call Option and the Call Option, on the applicable Redemption Date, the Company shall remit the applicable cash consideration to the Holder. The Holder shall deliver to the Company the certificates representing the Preferred Units as soon as practicable, following the applicable Redemption Date.

f) (i) In addition, the Company shall have the option (the “Low Price Redemption Option”) to redeem all of the Preferred Units if at any time (including the period prior to the Conversion Commencement Date), the closing price for the Common Units shall be less than $17.00 (as adjusted pursuant to Section 6(d)) (the “Low Price”) for 10 consecutive Trading Days (a “Low Price Trading Period”)

(ii) If a Low Price Trading Period shall have occurred, then, until the earlier of: (A) 5 Trading Days from the end of the Low Price Trading Period or (B) the first Trading Day following the Low Price Trading Period for which the closing price shall be above the Closing Price (as adjusted pursuant to Section

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6(d)), the Company may exercise the Trading Price Redemption Option by written notice to the Holder. Such notice (the “Low Price Redemption Notice”) shall specify the applicable redemption date (the “Low Price Redemption Date”) which shall be no more than 30 days from the date of the Low Price Redemption Notice.

(iii) On the Low Price Redemption Date, if prior to the Dividend Commencement Date, the Company shall pay to the Holder in cash the Liquidation Value of the Preferred Units plus an amount equal to the greater of: (A) an 8% annualized return on the Face Value from the issuance date; (B) an 8% annualized return on the Face Value for one quarter (collectively, the “Low Price Redemption Price”). If the Low Price Redemption Date occurs after the Dividend Commencement Date, the Company shall pay Holder the amount set forth above less the amount of dividend payments made on the Preferred Units.

(iv) The Company’s non-exercise of the Low Price Redemption Option shall not affect Holder’s right to convert Preferred Units pursuant to Section 6(a) above. If the Company exercises the Low Price Redemption Option, Holder may still convert any or all Preferred Units pursuant to the terms of Section 6(a) if Holder delivers a Conversion Notice prior to the Low Price Redemption Date and the Low Price Redemption Date occurs after the Conversion Commencement Date.

8. Voting Rights. In addition to all other requirements imposed by Delaware law, and all other voting rights granted under the Company’s Limited Partnership Agreement, the affirmative vote of a majority of the Company’s outstanding Preferred Units shall be necessary for repeal of this Certificate of Designations or the Certificate of Limited Partnership or Limited Partnership Agreement or any amendment to the Certificate of Limited Partnership or Limited Partnership Agreement (including any merger or consolidation) that may materially amend or change or adversely affect any of the rights, preferences, obligations or privileges of the Preferred Units provided, however, that Holders of Preferred Units who are affiliates of the Company (and the Company itself) shall not participate in such vote and the Preferred Units of such Holders shall be disregarded and deemed not to be outstanding for purposes of such vote.

9. Notices. The Company shall distribute to the Holders of Preferred Units copies of all notices, materials, annual and quarterly reports, proxy statements, information statements and any other documents distributed generally to the holders of Common Units of the Company, at such times and by such method as such documents are distributed to such holders of such Common Units.

10. Certificates.

a) The certificate(s) representing the Preferred Units held by any Holder of Preferred Units may be exchanged by such Holder at any time and from time to time for certificates with different denominations representing an equal aggregate number of Preferred Units, as reasonably requested by such Holder, upon surrendering the same. No service charge will be made for such registration or transfer or exchange. In the event that any Holder of

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Preferred Units notifies the Company that its certificate(s) therefor have been lost, stolen or destroyed, the Company shall promptly and without charge deliver replacement certificate(s) to such Holder, provided that such Holder executes and delivers to the Company an agreement reasonably satisfactory to the Company to indemnify the Company from any loss incurred by it in connection with such lost, stolen or destroyed certificate(s).

b) The certificate(s) representing the Preferred Units may be imprinted with a legend in substantially the following form:

“THIS CERTIFICATE IS NOT REQUIRED TO BE PHYSICALLY SURRENDERED TO THE COMPANY IN THE EVENT THAT THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE CONVERTED OR REDEEMED IN PART. AS A RESULT, FOLLOWING ANY CONVERSION OR REDEMPTION OF ANY PORTION OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE, THE SECURITIES REPRESENTED BY THIS CERTIFICATE MAY BE LESS THAN THE NUMBER OF UNITS INDICATED ON THIS CERTIFICATE. IF ANY SECURITIES ARE CONVERTED AS AFORESAID, THE HOLDER OF THIS CERTIFICATE MAY NOT TRANSFER ANY SECURITIES REPRESENTED BY THIS CERTIFICATE UNLESS AND UNTIL SUCH HOLDER FIRST PHYSICALLY SURRENDERS TO ATLAS PIPELINE PARTNERS, L.P. ALL CERTIFICATES REPRESENTING ANY SUCH SECURITIES WHICH HAVE PREVIOUSLY BEEN CONVERTED IN WHOLE OR IN PART, WHEREUPON ATLAS PIPELINE PARTNERS WILL FORTHWITH ISSUE AND DELIVER UPON THE ORDER OF SUCH HOLDER NEW CERTIFICATE(S) EVIDENCING SUCH SECURITIES THEN HELD BY SUCH HOLDER.”

11. Rank. For the avoidance of doubt, and notwithstanding anything contained herein to the contrary, the Preferred Units shall, with respect to dividends, other distributions and distributions upon the liquidation, winding-up and dissolution of the Company, rank senior and prior to Common Units and each other class of equity securities of the Company, including other preferred units and Incentive Distribution Rights, whether currently issued or issued in the future, other than the Class B Preferred Units.

12. No Reissuance. No Preferred Units acquired by the Company by reason of redemption, purchase, conversion or otherwise shall be reissued.

13. No Pari Passu or Senior Securities. So long as any Preferred Units remain outstanding, the Company and its subsidiaries shall not, without the affirmative vote of the Holders of at least 75% of the outstanding Preferred Units, issue any equity securities ranking pari passu with or senior to the Preferred Units with respect to liquidation preference, dividends, the timing of redemption or voting rights, except that the Company may issue up to an additional 10,000 Class B Preferred Units pursuant to the option granted in the Class B Preferred Unit Purchase Agreement, dated December 30, 2008, between the Company and Atlas Pipeline Holdings, L.P.

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14. Severability of Provisions. If any right, preference or limitation of the Preferred Units set forth in this Certificate of Designations (as this Certificate of Designations may be amended from time to time) is invalid, unlawful or incapable of being enforced by reason of any rule or law or public policy, all other rights, preferences and limitations set forth in this Certificate of Designations, which can be given effect without the invalid, unlawful or unenforceable right, preference or limitation shall nevertheless remain in full force and effect, and no right, preference or limitation herein set forth be deemed dependent upon any such other right, preference or limitation unless so expressed herein.

*  *  *  *  *

[Signature Page Follows]

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IN WITNESS WHEREOF, this Second Amended and Restated Certificate of Designations of the Company has been duly executed this 27th day of January, 2009.

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EXHIBIT A

(To be Executed by Holder

in order to Convert Preferred Units)

CONVERSION NOTICE

FOR

12% CUMULATIVE CONVERTIBLE PREFERRED UNITS

The undersigned, as a holder (“Holder”) of 12% Cumulative Convertible Preferred Units (“Preferred Units”) of Atlas Pipeline Partners, L.P. (the “Company”), hereby irrevocably elects to convert                                  Preferred Units for Common Units of the Company according to the terms and conditions of the Certificate of Designations for the Preferred Units as of the date written below. The undersigned hereby requests that certificates for the Common Units to be issued to the undersigned pursuant to this Conversion Notice be issued in the name of, and delivered to, the undersigned or its designee as indicated below. No fee will be charged to the Holder of Preferred Units for any conversion. Capitalized terms used herein and not otherwise defined shall have the meanings ascribed thereto in the Certificate of Designations.

If Common Units are to be issued to a person other than Holder,

Holder’s signature must be guaranteed below:

SIGNATURE GUARANTEED BY:

THE COMPUTATION OF NUMBER OF COMMON UNITS TO BE RECEIVED IS SET FORTH ON PAGE 2 OF THE CONVERSION NOTICE.

Page 1 of Conversion Notice

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COMPUTATION OF NUMBER OF COMMON UNITS TO BE RECEIVED

If the conversion is not being settled by DTC, please issue and deliver                      certificate(s) for Common Units in the following amount(s):

If the Holder is receiving certificate(s) for Preferred Units upon the conversion, please issue and deliver                      certificate(s) for Preferred Units in the following amounts: