Nuveen New Jersey Premium Income Municipal Fund (NNJ) CORRESP Correspondence with SEC

Nuveen Securities, LLC

333 West Wacker Drive

Chicago, IL 60606

P: 312. 917.7700

www.nuveen.com

July 30, 2013

VIA EDGAR

U.S. Securities and Exchange Commission

100 F Street, NE

Washington, DC 20549

Attn: Mr. Kieran Brown

Re: Request for Acceleration of the Effective Date of Nuveen New Jersey Premium Income Municipal Fund, Inc. (the “Fund”):Pre-Effective Amendment Number 2 Under the Securities Act of 1933 and Amendment No. 7 Under the Investment Company Act of 1940, Filed on Form N-2 on July 11, 2013 (File Nos. 333-187009 and 811-07118)

Dear Mr. Brown:

Pursuant to Rule 461 under the Securities Act of 1933, as amended, we hereby request that the effective date of the above-captioned Registration Statement be declared effective as of 9:00 a.m. ET on Wednesday, July 31, 2013, or as soon thereafter as practicable.

In connection with this request, Nuveen Securities, LLC, the underwriter for the Fund, has also signed this letter requesting acceleration.

Very truly yours,

Nuveen New Jersey Premium Income Municipal Fund, Inc.		Nuveen Securities, LLC
	/s/ Gifford R. Zimmerman		/s/ Gifford R. Zimmerman
By:	Gifford R. Zimmerman	By:	Gifford R. Zimmerman
Title:	Chief Administrative Officer	Title:	Managing Director, Assistant Secretary and Associate General Counsel