AMENDMENT NO. 1 TO INVESTOR RIGHTS AGREEMENT

Exhibit 4.1

AMENDMENT NO. 1 TO INVESTOR RIGHTS AGREEMENT

     This Amendment No. 1 to Investor Rights Agreement (this “Amendment”) is made and entered into effective as of June 24, 2005, by and among FRC-WPP NRP Investment L.P., a Delaware limited partnership (the “Investor”), Natural Resource Partners L.P., a Delaware limited partnership (the “Company”), NRP (GP) LP, a Delaware limited partnership (“NRP (GP) LP”), and GP Natural Resource Partners LLC, a Delaware limited liability company (the “General Partner”, and collectively with the Company and NRP (GP) LP, the “NRP Parties”), and amends the Investor Rights Agreement dated December 22, 2003 by and among the Investor and each of the NRP Parties (the “Agreement”).

R E C I T A L S

     A. The Company is a limited partnership engaged in the business of owning and managing coal properties (the “Business”). NRP (GP) LP is the general partner of the Company. The General Partner is the general partner of NRP (GP) LP.

     B. The parties hereto entered into the Agreement in connection with the Investor’s purchase of 4,796,920 subordinated units of the Company (the “Subordinated Units”).

     C. In connection with the Company’s registration of its subordinated units pursuant to Section 12 of the Securities and Exchange Act of 1934, as amended, and the registration statement on Form S-3 to be filed by the Company with the U.S. Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended, registering for resale the Subordinated Units and the common units of the Company (“Common Units”) issuable upon conversion of the Subordinated Units, the parties hereto wish to amend the Agreement as set forth below.

     NOW, THEREFORE, in consideration of the foregoing recitals, the mutual promises hereinafter set forth, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree to amend the Agreement as follows:

     1. The definition of the term “Registrable Securities” as set forth in Section 4.1(c) of the original Agreement is hereby deleted and replaced by the following language:

     “(c) Registrable Securities. The term “Registrable Securities” means (i) all subordinated units of the Company now held or hereinafter acquired by the Investor; (ii) all Common Units of the Company issued upon conversion of the Subordinated Units held by the Investor or the conversion of any additional subordinated units of the Company hereinafter acquired by the Investor; and (iii) any additional Common Units hereinafter otherwise acquired by the Investor. Notwithstanding the foregoing, “Registrable Securities” shall exclude any Registrable Securities sold by a person in a transaction in which rights under this Section 4 are not assigned in accordance with this Agreement or any Registrable Securities sold in a public offering, whether sold pursuant to Rule 144 promulgated under the Securities Act, or in a registered offering, or otherwise.”

1

     2. Section 4.2(b) of the original Agreement is hereby deleted and replaced with the following language:

     “(b) Underwriting. If the Requesting Holders intend to distribute the Registrable Securities covered by its request by means of an underwritten offering, then it shall so advise the Company as a part of the Demand Notice, and the Company shall include such information in the Request Notice. In such event, the right of any Holder to include his or her Registrable Securities in such registration shall be conditioned upon such Holder’s participation in such underwriting and the inclusion of such Holder’s Registrable Securities in the underwriting (unless otherwise mutually agreed by the Requesting Holders and such Holder) as provided herein. The Company and all Holders proposing to distribute their securities through such underwriting shall enter into an underwriting agreement in customary form with the managing underwriter or underwriters selected for such underwriting by the Requesting Holders and reasonably acceptable to the Company. All Holders, whether or not they are participating in such offering, and the Company agree not to effect any sale, transfer, assignment, pledge or conveyance of (including, without limitation, taking any short position in) Common Units or subordinated units (or any securities of the Company exchangeable or convertible into Common Units) as follows: (i) with respect to an offering that includes subordinated units, during the 90-day period beginning on the effective date of a registration statement filed by the Company (except as part of that Registration) pursuant to this Agreement; and (ii) with respect to any offering that does not include subordinated units, during the 180-day period beginning on the effective date of a registration statement filed by the Company (except as part of that Registration) pursuant to this Agreement. Notwithstanding any other provision of this Section 4.2 or Section 4.3, if the managing underwriter(s) determine in good faith that marketing factors require a limitation of the number of securities to be underwritten, then the Company shall so advise all Holders of Registrable Securities that would otherwise be registered and underwritten pursuant hereto, and the managing underwriter(s) may exclude shares of the Registrable Securities from the registration and the underwriting, and the number of shares that will be included in the registration and the underwriting shall be allocated, first to the Requesting Holders and to each of the Holders requesting inclusion of their Registrable Securities in such registration statement pursuant to Section 4.3. on a pro rata basis based on the total number of Registrable Securities then held by the Requesting Holders and each such Holder, and second to the Company and any other holders of Common Units or subordinated units that are participating in the registration (on a basis to be determined between the Company and any such other holders).”

     3. Section 4.2(c) of the original Agreement is hereby deleted and replaced with the following language:

     “(c) Maximum Number of Demand Registrations. The Company shall be obligated to effect only 2 (two) such registrations pursuant to this Section 4.2 (including any shelf registrations requested under this Section 4.2). A Registration shall be effected for purposes of this Section 4.2(c) when and if a registration statement is declared effective by the Securities and Exchange Commission and the distribution of securities thereunder has been completed without the occurrence of any stop order or proceeding relating thereto suspending the effectiveness of the Registration.”

2

     4. Section 4.2(d) of the original Agreement is hereby deleted and replaced with the following language:

     “(d) Expenses: All expenses incurred in connection with any registration proposed pursuant to this Section 4.2, including without limitation underwriters’ and brokers’ discounts and commissions relating to Registrable Securities sold by the Holders, all federal and “blue sky” registration, filing and qualification fees, printer’s and accounting fees, fees and expenses of counsel for the Holders, reasonable fees and expenses of one counsel to the Company (selected by the Company), reasonable fees and expenses of one counsel to the Conflicts Committee of the General Partner (or another special committee of the General Partner convened to review such registration) selected by such committee, and reasonable road show expenses (including aircraft charter fees (if any) and other travel expenses) shall be borne by the Holders. Each Holder participating in a registration pursuant to this Section 4.2 shall bear such Holder’s proportionate share (based on the total number of shares sold in such registration) of all such expenses.”

     5. The following two sentences shall be added to the end of Section 4.3 of the original Agreement:

     “With respect to any registration statement referenced in a Piggyback Notice, the registration rights afforded to Holders in this Section 4.3 shall only apply to the type of Registrable Securities to be included in such registration statement prior to the exercise of any rights under this Section 4.3. For example, where a registration statement listed in a Piggyback Notice is to effect a public offering of Common Units but not subordinated units, each Holder under this Section 4.3 will only have the right to include in such registration statement Common Units then held by such Holder (and such Holder shall not have the right to include therein any subordinated units).”

     6. Section 4.3(b) of the original Agreement is hereby deleted and replaced with the following language:

     “(b) Expenses. All expenses incurred in connection with a registration pursuant to this Section 4.3 (excluding underwriters’ and brokers’ discounts and commissions relating to Registrable Securities sold by the Holders, and further excluding fees and disbursements of counsel for Holders), including, without limitation all federal and “blue sky” registration, filing and qualification fees, printers’ and accounting fees, and fees and disbursements of counsel for the Company, shall be borne by the Company.”

     7. Section 4.4(a) of the original Agreement is hereby deleted and replaced with the following language

     “(a) Registration Statement. Prepare and file with the SEC a registration statement (including a “shelf registration statement” pursuant to Rule 415 on Form S-3, if eligible and requested by the Holders) with respect to such Registrable Securities and use its commercially reasonable efforts to cause such registration statement to become effective and to keep any such registration statement effective for the shorter of (i) in the case of any registration

3

pursuant to Rule 415 on Form S-3, a period of two years, or in the case of any other registration, a period of 180 days (the “Registration Period”), as may be extended pursuant to clause (f) below, or (ii) until all of such Registrable Securities included in such registration statement have been sold.”

     8. Other than expressly set forth in this Amendment, all terms and conditions of the original Agreement shall remain unchanged and in full force and effect.

     9. This Amendment may be executed in one or more counterparts, each of which shall be deemed to be an original but all of which shall constitute one and the same agreement.

[Intentionally Blank — Next Page is the Signature Page]

4

     IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of the date and year first above written.

5