Exhibit 10.13 NEWMIL BANK DIRECTOR DEFERRED COMPENSATION AGREEMENT

Exhibit 10.13

NEWMIL BANK

DIRECTOR DEFERRED COMPENSATION AGREEMENT

THIS DIRECTOR DEFERRED COMPENSATION AGREEMENT (this “Agreement”) is made as of this 22 day of January 2003, by and between NewMil Bank, a Connecticut-chartered, FDIC-insured savings bank located in New Milford, Connecticut (the “Bank”), and Joseph Carlson II (the “Director”).

WHEREAS, the Director serves as a director of NewMil Bank and NewMil Bancorp, Inc.,

WHEREAS, the Director and the Bank intend by this Agreement to provide for payment of benefits if the Director’s service terminates within 12 months after a change in control of NewMil Bancorp, Inc., and

NOW THEREFORE, in consideration of these premises and other good and valuable consideration the receipt and sufficiency of which are hereby acknowledged, the Director and the Bank hereby agree as follows:

ARTICLE 1

DEFINITIONS

Whenever used in this Agreement, the following words and phrases shall have the meanings specified:

1.1 “Change in Control” means if any one of the following events occurs —

(a) Merger: NewMil Bancorp, Inc. merges into or consolidates with another corporation, or merges another corporation into NewMil Bancorp, Inc., and as a result less than a majority of the combined voting power of the resulting corporation immediately after the merger or consolidation is held by persons who were stockholders of NewMil Bancorp, Inc. immediately before the merger or consolidation. For purposes of this Agreement, the term person means an individual, corporation, partnership, trust, association, joint venture, pool, syndicate, sole proprietorship, unincorporated organization or other entity,

(b) Acquisition of Significant Share Ownership: a report on Schedule 13D or another form or schedule (other than Schedule 13G) is filed or is required to be filed under Sections 13(d) or 14(d) of the Securities Exchange Act of 1934, if the schedule discloses that the filing person or persons acting in concert has or have become the beneficial owner of 25% or more of a class of NewMil Bancorp, Inc.’s voting securities, but this clause (b) shall not apply to beneficial ownership of NewMil Bancorp, Inc. voting shares held in a fiduciary capacity by an entity of which NewMil Bancorp, Inc. directly or indirectly beneficially owns 50% or more of its outstanding voting securities,

(c) Change in Board Composition: during any period of two consecutive years, individuals who constitute NewMil Bancorp, Inc.’s Board of Directors at the beginning of the two-year period cease for any reason to constitute at least a majority of NewMil Bancorp, Inc.’s Board of Directors; provided, however, that — for purposes of this clause (c) — each director who is first elected by the board (or first nominated by the board for election by stockholders) by a vote of at least two-thirds (2/3) of the directors who were directors at the beginning of the period shall be deemed to have been a director at the beginning of the two-year period, or

(d) Sale of Assets: NewMil Bancorp, Inc. sells to a third party all or substantially all of NewMil Bancorp, Inc.’s assets. For purposes of this Agreement, sale of substantially all of NewMil Bancorp, Inc.’s assets includes sale of the shares or assets of NewMil Bank.

1.2 “Code” means the Internal Revenue Code of 1986, as amended.

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1.3 “Compensation” means the total directors’ fees payable to the Director during a Plan Year.

1.4 “Deferral Account” means the Bank’s accounting of the Director’s accumulated Deferrals, plus accrued interest.

1.5 “Deferrals” means the amount of the Director’s Compensation that the Director elects to defer according to this Agreement.

1.6 “Disability” means the Director’s inability to perform substantially all normal duties of a director, as determined by the Bank’s Board of Directors in its sole discretion. As a condition to any benefits, the Bank may require the Director to submit to such physical or mental evaluations and tests as the Board of Directors deems appropriate.

1.7 “Effective Date” means January 22, 2003.

1.8 “Election Form” means the Form attached as Exhibit 1.

1.9 “Normal Retirement Age” means the Director’s 65^th birthday.

1.10 “Normal Retirement Date” means the later of the Normal Retirement Age or Termination of Service.

1.11 “Plan Year” means the calendar year.

1.12 “Termination for Cause” means the Bank’s board of directors or a duly authorized committee of the board of directors determines at any time that the Director will not be nominated by the board or committee for reelection as a director of NewMil Bancorp after the expiration of his current term, or if the Director is removed as a director of the Bank, in either case because of the Director’s —

1.13 “Termination of Service” means that the Director ceases to be a member for the Bank’s Board of Directors for any reason whatsoever.

ARTICLE 2

DEFERRAL ELECTION

2.1 Initial Election. The Director shall make an initial deferral election under this Agreement by filing with the Bank a signed Election Form within 30 days after the Effective Date of this Agreement. The Election Form shall set forth the amount of Compensation to be deferred and shall be effective to defer Compensation earned after the date the Election Form is received by the Bank.

2.2 Election Changes. Upon the Bank’s approval, the Director may modify the amount of Compensation to be deferred annually by filing a new Election Form with the Bank prior to the beginning of the Plan Year in which the Compensation is to be deferred. The modified deferral election shall not be effective until the calendar year following the year in which the subsequent Election Form is received and approved by the Bank.

ARTICLE 3

DEFERRAL ACCOUNT

3.1 Establishing and Crediting. The Bank shall establish a Deferral Account on its books for the Director and shall credit to the Deferral Account the following amounts:

3.1.2 Deferrals. The portion of the Compensation deferred by the Director as of the time the Compensation would have otherwise been paid to the Director.

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3.1.3 Interest. At the end of each Plan Year under this Agreement, but only until commencement of benefit payments under this Agreement, unless otherwise stated, interest is to be credited on the account balance at an annual rate of interest for that Plan Year, compounded monthly, equal to the monthly average yield on United States Treasury securities adjusted to a constant maturity of five years as published by the Board of Governors of the Federal Reserve System in statistical release H.15 (the “Index”). The interest credited for a Plan Year shall be based upon the Index during the month of December for the current Plan Year.

3.2 Statement of Accounts. The Bank shall provide to the Director, within 120 days after the end of each Plan Year, a statement setting forth the Deferral Account balance.

3.3 Accounting Device Only. The Deferral Account is solely a device for measuring amounts to be paid under this Agreement. The Deferral Account is not a trust fund of any kind. The Director is a general unsecured creditor of the Bank for the payment of benefits. The benefits represent the mere Bank promise to pay such benefits. The Director’s rights are not subject in any manner to anticipation, alienation, sale, transfer, assignment, pledge, encumbrance, attachment, or garnishment by the Director’s creditors.

ARTICLE 4

BENEFITS DURING LIFETIME

4.1 Normal Retirement Benefit. Upon the Normal Retirement Date, the Bank shall pay to the Director the benefit described in this Section 4.1 in lieu of any other benefit under this Agreement.

4.1.1 Amount of Benefit. The benefit under this Section 4.1 is the Deferral Account balance at the Director’s Normal Retirement Date.

4.1.2 Payment of Benefit. The Bank shall pay the benefit to the Director in the form elected by the Director in the Election Form commencing with the month following the Director’s Normal Retirement Date. If the Director elects payment of the benefit as other than a lump sum, the Bank will continue to credit interest pursuant to the formula of Section 3.1.3, compounded monthly, on the remaining account balance during any applicable installment period.

4.2 Early Retirement Benefit. Upon Termination of Service prior to the Normal Retirement Age for reasons other than death, Change in Control or Disability, the Bank shall pay to the Director the benefit described in this Section 4.2 in lieu of any other benefit under this Agreement.

4.2.1 Amount of Benefit. The benefit under this Section 4.2 is the Deferral Account balance at the Director’s Termination of Service.

4.2.2 Payment of Benefit. The Bank shall pay the benefit to the Director in the form elected by the Director in the Election Form commencing with the month following the Director’s Normal Retirement Age. If the Director elects payment of the benefit as other than a lump sum, the Bank will continue to credit interest pursuant to the formula of Section 3.1.3, compounded monthly, on the remaining account balance during any applicable installment period.

4.3 Disability Benefit. If the Director terminates service due to Disability prior to Normal Retirement Age, the Bank shall pay to the Director the benefit described in this Section 4.3 in lieu of any other benefit under this Agreement.

4.3.1 Amount of Benefit. The benefit under this Section 4.3 is the Deferral Account balance at the Director’s Termination of Service.

4.3.2 Payment of Benefit. The Bank shall pay the benefit to the Director in the form elected by the Director in the Election Form commencing with the month following the Director’s Termination of Service. If the Director elects payment of the benefit as other than a lump sum, the Bank will

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continue to credit interest pursuant to the formula of Section 3.1.3, compounded monthly, on the remaining account balance during any applicable installment period.

4.4 Change in Control Benefit. Upon a Change in Control, followed within twelve (12) months by the Director’s Termination of Service for reasons other than death or Disability, the Bank shall pay to the Director the benefit described in this Section 4.4 in lieu of any other benefit under this Agreement.

4.4.1 Amount of Benefit. The benefit under this Section 4.4 is the Deferral Account balance on the Director’s Termination of Service.

4.4.2 Payment of Benefit. The Bank shall pay the benefit to the Director in a lump sum within 30 days after the Director’s Termination of Service.

4.5 Payout of Normal Retirement Benefit, Early Termination Benefit, or Disability Benefits after a Change in Control. If a Change in Control occurs when the Director is receiving benefits provided by Sections 4.1, 4.2 or 4.3 of this Agreement, the Bank shall pay the remaining benefits to the Director in a single lump sum within three days after the Change in Control. The lump-sum payment shall be an amount equal to the Director’s Deferral Account balance remaining unpaid.

4.6 Hardship Distribution. Upon the Board of Director’s determination (following petition by the Director) that the Director has suffered an unforeseeable financial emergency, the Bank shall distribute to the Director all or a portion of the Deferral Account balance as determined by the Bank.

ARTICLE 5

DEATH BENEFITS

5.1 Death During Active Service. If the Director dies while in the service of the Bank, the Bank shall pay to the Director’s beneficiary the early retirement benefit described in Section 4.2 in lieu of any other benefit under this Agreement.

5.2 Death During Payment of a Benefit. If the Director dies after any benefit payments have commenced under this Agreement but before receiving all such payments, the Bank shall pay the remaining benefits to the Director’s beneficiary in a lump sum distribution. The lump sum distribution will equal the Director’s Deferral Account as of the time of death.

5.3 Death After Termination of Service But Before Benefit Payments Commence. If the Director is entitled to benefit payments under this Agreement but dies prior to the commencement of said benefit payments, the Bank shall pay the same benefit payments to the Director’s beneficiary that the Director was entitled to prior to death except that the benefit payments shall be paid in a lump sum distribution equal to the Director’s Deferral Account balance on the first day of the month following the date of the Director’s death.

ARTICLE 6

BENEFICIARIES

6.1 Beneficiary Designations. The Director shall designate a beneficiary by filing a written designation with the Bank. The Director may revoke or modify the designation at any time by filing a new designation. However, designations will only be effective if signed by the Director and received by the Bank during the Director’s lifetime. The Director’s beneficiary designation shall be deemed automatically revoked if the beneficiary predeceases the Director or if the Director names a spouse as beneficiary and the marriage is subsequently dissolved. If the Director dies without a valid beneficiary designation, all payments shall be made to the Director’s estate.

6.2 Facility of Payment. If a benefit is payable to a minor, to a person declared incompetent, or to a person incapable of handling the disposition of his or her property, the Bank may pay such benefit to the guardian, legal representative or person having the care or custody of such minor, incompetent person or incapable person. The Bank may require proof of incompetence, minority or guardianship as it

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may deem appropriate prior to distribution of the benefit. Such distribution shall completely discharge the Bank from all liability with respect to such benefit.

ARTICLE 7

GENERAL LIMITATIONS

7.1 Termination for Cause. Notwithstanding any provision of this Agreement to the contrary, the Bank shall not pay any benefit under this Agreement that is in excess of the Director’s Deferrals (i.e., the deferred compensation account balance under Section 3.1.1, the amount deferred under Section 3.1.2, and the interest earned on the Deferral Account) if Termination of Service is due to the Director’s actions resulting in Termination for Cause. The Director’s Deferrals shall be paid to the Director in a manner to be determined by the Bank. No interest shall be credited to the Deferrals during any applicable installment period.

7.2 General. Notwithstanding anything to the contrary contained in this Agreement, the Director is entitled to only one benefit which shall be determined by the first event to occur which is dealt with by this Agreement. Subsequent occurrence of events dealt with by this Agreement shall not entitle the Director or his or her beneficiaries to other or further benefits under this Agreement.

7.3 Tax Consequences. The Bank does not insure or guarantee the tax consequences of payments provided hereunder for matters beyond its control, and the Director certifies that his decision to reduce and defer receipt of his compensation is not due to any reliance upon financial, tax or legal advice given by the Bank, and of its employees, agents, accountants or legal advisors.

ARTICLE 8

CLAIMS AND REVIEW PROCEDURES

8.1 Claims Procedure. The Bank shall notify any person or entity that makes a claim for benefits under this Agreement (the “Claimant”) in writing, within 90 days of Claimant’s written application for benefits, of his or her eligibility or non-eligibility for benefits under this Agreement. If the Bank determines that the Claimant is not eligible for benefits or full benefits, the notice shall set forth (a) the specific reasons for such denial, (b) a specific reference to the provisions of this Agreement on which the denial is based, (c) a description of any additional information or material necessary for the Claimant to perfect his or her claim, and a description of why it is needed, and (d) an explanation of this Agreement’s claims review procedure and other appropriate information as to the steps to be taken if the Claimant wishes to have the claim reviewed. If the Bank determines that there are special circumstances requiring additional time to make a decision, the Bank shall notify the Claimant of the special circumstances and the date by which a decision is expected to be made, and may extend the time for up to an additional 90 days.

8.2 Review Procedure. If the Claimant is determined by the Bank not to be eligible for benefits, or if the Claimant believes that he or she is entitled to greater or different benefits, the Claimant shall have the opportunity to have such claim reviewed by the Bank by filing a petition for review with the Bank within 60 days after receipt of the notice issued by the Bank. Said petition shall state the specific reasons, which the Claimant believes entitle him or her to benefits or to greater or different benefits. Within 60 days after receipt by the Bank of the petition, the Bank shall afford the Claimant (and counsel, if any) an opportunity to present his or her position to the Bank verbally or in writing, and the Claimant (or counsel) shall have the right to review the pertinent documents. The Bank shall notify the Claimant of its decision in writing within the 60-day period, stating specifically the basis of its decision, written in a manner to be understood by the Claimant and the specific provisions of this Agreement on which the decision is based. If, because of the need for a hearing, the 60-day period is not sufficient, the decision may be deferred for up to another 60 days at the election of the Bank, but notice of this deferral shall be given to the Claimant.

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ARTICLE 9

AMENDMENTS AND TERMINATION

This Agreement may be amended or terminated only by a written agreement signed by the Bank and the Director. In no event shall this Agreement be terminated without payment to the Director of the Deferral Account balance attributable to the Director’s Deferrals and interest credited on such amounts unless the Agreement terminates as a result of Termination for Cause in which event the Director forfeits the interest credited on the Director’s Deferrals.

Notwithstanding the previous paragraph in this Article 9, the Bank may amend or terminate this Agreement at any time if, pursuant to legislative, judicial or regulatory action, continuation of this Agreement would (a) cause benefits to be taxable to the Director prior to actual receipt, or (b) result in significant financial penalties or other significantly detrimental ramifications to the Bank (other than the financial impact of paying the benefits). In no event shall this Agreement be terminated under this paragraph without payment to the Director of the Deferral Account balance attributable to the Director’s Deferrals and interest credited on such amounts.

ARTICLE 10

MISCELLANEOUS

10.1 Binding Effect. This Agreement shall bind the Director and the Bank and their beneficiaries, survivors, executors, administrators and transferees.

10.2 No Guarantee of Employment. This Agreement is not a contract for services. It does not give the Director the right to remain a director of the Bank, nor does it interfere with shareholders’ right to replace the Director. It also does not require the Director to remain a director nor interfere with the Director’s right to terminate services at any time.

10.3 Non-Transferability. Benefits under this Agreement cannot be sold, transferred, assigned, pledged, attached or encumbered in any manner.

10.4 Tax Withholding. The Bank shall withhold any taxes required to be withheld from the benefits provided under this Agreement.

10.5 Applicable Law. This Agreement and all rights hereunder shall be governed by the laws of Connecticut, except to the extent the laws of the United States of America otherwise require.

10.6 Unfunded Arrangement. The Director and the Director’s beneficiary are general unsecured creditors of the Bank for the payment of benefits under this Agreement. The benefits represent the mere promise by the Bank to pay such benefits. The rights to benefits are not subject in any manner to anticipation, alienation, sale, transfer, assignment, pledge, encumbrance, attachment, or garnishment by creditors. Any insurance on the Director’s life is a general asset of the Bank to which the Director and the Director’s beneficiary have no preferred or secured claim.

10.7 Reorganization. The Bank shall not merge or consolidate into or with another Bank, or reorganize, or sell substantially all of its assets to another Bank, firm, or person unless such succeeding or continuing Bank, firm, or person agrees to assume and discharge the obligations of the Bank under this Agreement. Upon the occurrence of such event, the term “Bank” as used in this Agreement shall be deemed to refer to the successor or survivor Bank.

10.8 Entire Agreement. This Agreement constitutes the entire agreement between the Bank and the Director as to the subject matter hereof. No rights are granted to the Director under this Agreement other than those specifically set forth herein. This Agreement supersedes and replaces in its entirety the Deferred Compensation Agreement with Director dated between the Director and the Bank, as successor to Nutmeg.

10.9 Administration. The Bank shall have powers which are necessary to administer this Agreement, including but not limited to —

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10.10 Named Fiduciary. The Bank shall be the named fiduciary and plan administrator under this Agreement. The named fiduciary may delegate to others certain aspects of the management and operation responsibilities of the plan including the employment of advisors and the delegation of ministerial duties to qualified individuals.

IN WITNESS WHEREOF, the Director and a duly authorized Bank officer have executed this Agreement as of the day and year first written above.

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Exhibit 1

NEWMIL BANK

DIRECTOR DEFERRED COMPENSATION AGREEMENT

Deferral Election

I elect to defer my Compensation under this Agreement with the Bank, as follows:

Form of Benefit

I elect to receive benefits under the Director Deferred Compensation Agreement in the following form:

[Initial One]

             Lump Sum

             Equal monthly installments for One Hundred Twenty (120) months

I understand that I may not change the form of benefit elected, even if I later change the amount of my deferrals under the Director Deferred Compensation Agreement without written approval of the Board of Directors of the Bank.

Upon the Bank’s approval, I understand that I may change the amount and duration of my deferrals by filing a new election form with the Bank; provided, however, that any subsequent election will not be effective until the calendar year following the year in which the new election is received by the Bank.

Received by the Bank this 22 day of January 2003.

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Beneficiary Designation

NEWMIL BANK

DIRECTOR DEFERRED COMPENSATION AGREEMENT

I designate the following as beneficiary of benefits under this Director Deferred Compensation Agreement payable following my death:

Primary:                                                                                                                                                                                                                                           

Contingent:                                                                                                                                                                                                                                     

I understand that I may change these beneficiary designations by filing a new written designation with the Bank. I further understand that the designations will be automatically revoked if the beneficiary predeceases me, or, if I have named my spouse as beneficiary and our marriage is subsequently dissolved.

Received by the Bank this 22 day of January 2003.

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