NUVEEN NEW JERSEY PREMIUM INCOME MUNICIPAL FUND, INC. Chicago, Illinois 60606

Exhibit h.1

NUVEEN NEW JERSEY PREMIUM INCOME MUNICIPAL FUND, INC.

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April 9, 2013

Nuveen Securities, LLC

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Re: Distribution Agreement Relating to At-the-Market Offerings

Ladies and Gentlemen:

Nuveen New Jersey Premium Income Municipal Fund, Inc. is a Minnesota corporation operating as a closed-end management investment company (hereinafter referred to as the “Fund”). The Fund has filed a registration statement on Form N-2 (File Nos. File Nos. 333-187009 and 811-07118) (the “Registration Statement”) pursuant to the Investment Company Act of 1940, as amended, and the Securities Act of 1933, as amended, to register additional shares of common stock of the Fund, which may be issued and sold from time to time through various specified transactions, including at-the-market (“ATM”) offerings.

You have informed us that Nuveen Securities, LLC is registered as a broker-dealer under the provisions of the Securities Exchange Act of 1934 and is a member in good standing of the Financial Industry Regulatory Authority, Inc. You have indicated your desire to act as distributor for the Fund’s shares of common stock issued pursuant to the Registration Statement. We have been authorized by the Fund to execute and deliver this Agreement to you by a resolution of our Board of Directors (the “Directors”) adopted at a meeting of the Directors, at which a majority of Directors, including a majority of our Directors who are not otherwise interested persons of our investment manager or its related organizations, were present and voted in favor of said resolution approving this Agreement.

1. APPOINTMENT OF DISTRIBUTOR. Upon the execution of this Agreement and in consideration of the agreements on your part herein expressed and upon the terms and conditions set forth herein, we hereby appoint you as the distributor for up to 1.2 million of the shares of common stock of the Fund to be issued pursuant to the Registration Statement through ATM offerings (the “Shares”) and agree that we will issue such Shares as you may sell. You agree to use reasonable efforts to identify opportunities for the sale of Shares, but you are not obligated to sell any specific number of the Shares. The Shares will only be sold on such days as shall be agreed to by you and the Fund.

2. SELECTED DEALERS. You may enter into selected dealer agreements, on such terms and conditions as you determine are not inconsistent with this Agreement, with broker-dealers to act as your agent to effect the sale of the Shares. Such selected broker-dealers shall sell Shares only at market prices subject to a minimum price to be established each day by you and the Fund (see paragraph 3 below). This Agreement shall not be construed as authorizing any

dealer or other person to accept orders for sale on our behalf or to otherwise act as our agent for any purpose. You shall not be responsible for the acts of other dealers or agents except as and to the extent that they shall be acting for you or under your direction or authority.

3. SHARE PRICE. The price per Share shall be determined by reference to trades on the Fund’s primary exchange. In no event shall the price be less than the current net asset value per share plus the per share amount of the commission to be paid to you (the “Minimum Price”). You shall suspend the sale of Shares if the per share price of the Shares is less than the Minimum Price.

4. SALES COMMISSION.

(a) You shall be entitled to receive a sales commission from the Fund of 1.0% of the gross sales price per Share of the Shares sold.

(b) You may pay to selected broker-dealers such selling agent commissions (not exceeding 80% of the total sales commission) (the “ATM Sales Agent Commission”) as you shall deem advisable, which shall be payable from the commissions payable to you under Section 4(a) above.

5. FURNISHING OF INFORMATION. We will furnish you with copies of the Registration Statement, and we warrant that the statements therein contained are true and correct as of the date of the Registration Statement, as it may be amended or supplemented from time to time. We will also furnish you with such other information that you may reasonably request for use in connection with the distribution of the Shares, including, at least annually, audited financial statements of our books and accounts certified by independent public accountants.

6. CONDUCT OF BUSINESS. Other than the currently effective Prospectus and Statement of Additional Information, you will not use any sales materials or statements except literature or advertising that conforms to the requirements of federal and state securities laws and regulations and that have been filed, where necessary, with the appropriate regulatory authorities. You will furnish us with copies of all material prior to their use and no such material shall be published if we shall reasonably and promptly object.

You shall comply with the applicable federal and state laws and regulations where our shares are offered for sale and conduct your affairs with us and with dealers, brokers or investors in accordance with the Conduct Rules of the Financial Industry Regulatory Authority, Inc.

7. OTHER ACTIVITIES. Your services pursuant to this Agreement shall not be deemed to be exclusive and you may render similar services and act as an underwriter, distributor, or dealer for other investment companies in the offering of their shares.

8. SUSPENSION OF SALES. We reserve the right at all times to suspend or limit the offering of the shares upon written notice to you and to reject any order in whole or in part.

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9. PAYMENT OF EXPENSES.

(a) You shall bear all expenses incurred by you in connection with your duties and activities under this Agreement including the payment to selected dealers of any sales commissions for sales of the Fund’s Shares.

(b) The Fund shall bear all costs and expenses of the Fund, including expenses (including legal fees) pertaining to the preparation and filing of the Registration Statement and Prospectus and any amendment or supplement thereto, and expenses pertaining to the preparation, printing and distribution of any reports or communications to shareholders, including Prospectuses and Statements of Additional Information, annual and interim reports, or proxy materials.

10. TERMINATION. This Agreement (i) may be terminated by the Fund at any time without the payment of any penalty and (ii) may be terminated by you at any time without the payment of any penalty. This Agreement shall remain in full force and effect unless terminated pursuant to this provision or by the mutual agreement of the parties.

11. MISCELLANEOUS. This Agreement shall be subject to the laws of the State of Illinois and shall be interpreted and construed to further and promote the operation of the Fund as a closed-end management investment company.

12. STANDARD OF CARE. You shall be responsible for exercising reasonable care in carrying out the provisions of this Agreement.

13. ARTICLES OF INCORPORATION AND LIMITATION OF LIABILITY. A copy of the Articles of Incorporation of the Fund is on file with the Secretary of State of the State of Minnesota, and notice is hereby given that this Agreement is executed by an officer of the Fund on behalf of the Directors, as directors and not individually, and that the obligations of this Agreement with respect to the Fund shall be binding upon the assets and properties of the Fund only and shall not be binding upon the assets or properties of the Directors, officers, employees, agents or shareholders of the Fund individually.

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If the foregoing meets with your approval, please acknowledge your acceptance by signing each of the enclosed counterparts hereof and returning such counterparts to us, whereupon this shall constitute a binding agreement as of the date first above written.

Very truly yours,

NUVEEN NEW JERSEY PREMIUM INCOME MUNICIPAL FUND, INC.

By:		/s/ ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
Name:		▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
Title:		Vice President and Secretary
Agreed to and Accepted:
NUVEEN SECURITIES, LLC
By:		/s/ ▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
Name:		▇▇▇▇▇ ▇. ▇▇▇▇▇▇▇▇
Title:		Managing Director

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