Ex h.10.

TORTOISE ENERGY INFRASTRUCTURE CORPORATION

COMMON STOCK ($0.001 PAR VALUE)

THIRD AMENDMENT

TO

CONTROLLED EQUITY OFFERING^SM SALES AGREEMENT

December 16, 2015

THIS THIRD AMENDMENT (this “Amendment”) to the Sales Agreement (defined below) is entered into on and as of December 16, 2015, by and among Tortoise Energy Infrastructure Corporation, a Maryland corporation (the “Fund”), Tortoise Capital Advisors, LLC, a Delaware limited liability company (the “Adviser”) and Cantor Fitzgerald & Co. (the “Agent”, and together with the Fund and Adviser, the “Parties”). Capitalized terms used and not defined in this Amendment have the meanings ascribed thereto in the Sales Agreement (as defined below).

WHEREAS, the Parties entered into that certain Controlled Equity Offering^SM Sales Agreement, dated April 23, 2012 (the “Original Sales Agreement”), with respect to the issuance and sale of shares of the Fund’s common stock, par value $0.001 per share having an aggregate gross sales price of up to $30,000,000 in at-the-market public offerings through the Agent;

WHEREAS, the Parties entered into that certain First Amendment to Controlled Equity Offering^SM Sales Agreement, dated November 27, 2013 (the “First Amendment”) in order to increase the Maximum Amount (as defined in the Original Sales Agreement) from $30,000,000 to $60,000,000;

WHERAS, the Parties entered into that certain Second Amendment to Controlled Equity Offering^SM Sales Agreement, dated October 1, 2015 (the “Second Amendment” and together with the Original Sales Agreement and the First Amendment, the “Sales Agreement”),

WHEREAS, the Parties desire to amend the Sales Agreement.

NOW THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, it is agreed as follows:

1. All references in the Sales Agreement to “September 30, 2015” are hereby changed to “December 14, 2015.”

2. Each of the Fund and the Adviser represent to the Agent that it has duly authorized, executed and delivered this Amendment.

3. Except as modified and amended in this Amendment, the Sales Agreement shall remain in full force and effect.

4. This Amendment shall be governed by and construed in accordance with the law governing the Sales Agreement.

5. This Amendment may be executed in multiple counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

[SIGNATURE PAGE FOLLOWS]

IN WITNESS WHEREOF, the Parties have caused this Amendment to be duly executed as of the date first above written.

Very truly yours,

TORTOISE ENERGY INFRASTRUCTURE CORPORATION

By:

Name:

Title:

TORTOISE CAPITAL ADVISORS, LLC

By:

Name:

Title:

ACCEPTED, as of the date first-above written:

CANTOR FITZGERALD & CO.

By:

Name:

Title:

Signature page to Third Amendment to Tortoise Energy Infrastructure Corporation (TYG) Sales Agreement