TORTOISE ENERGY INFRASTRUCTURE CORPORATION COMMON STOCK ($0.001 PAR VALUE) SIXTH AMENDMENT TO CONTROLLED EQUITY OFFERINGSM SALES AGREEMENT April 27, 2018

Exhibit 99.h.12

TORTOISE ENERGY INFRASTRUCTURE CORPORATION

COMMON STOCK ($0.001 PAR VALUE)

SIXTH AMENDMENT

TO

CONTROLLED EQUITY OFFERING^SM SALES AGREEMENT

April 27, 2018

THIS SIXTH AMENDMENT (this “Amendment”) to the Sales Agreement (defined below) is entered into on and as of April 27, 2018, by and among Tortoise Energy Infrastructure Corporation, a Maryland corporation (the “Fund”), Tortoise Capital Advisors, L.L.C., a Delaware limited liability company (the “Adviser”) and Cantor Xxxxxxxxxx & 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”);

WHEREAS, the Parties entered into that certain Second Amendment to Controlled Equity Offering^SM Sales Agreement, dated October 1, 2015 (the “Second Amendment”);

WHEREAS, the Parties entered into that certain Third Amendment to Controlled Equity Offering^SM Sales Agreement, dated December 16, 2015 (the “Third Amendment”);

WHEREAS, the Parties entered into that certain Fourth Amendment to Controlled Equity Offering^SM Sales Agreement, dated May 19, 2016 (the “Fourth Amendment”);

WHEREAS, the Parties entered into that certain Fifth Amendment to Controlled Equity Offering ^SM Sales Agreement, dated December 12, 2017 and together with the Original Sales Agreement, the First Amendment, the Second Amendment, the Third Amendment and the Fourth Amendment, the “Sales Agreement”); and

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 “May 2, 2017” are hereby changed to “April 27, 2018.”

2.          The definition of “Investment Advisory Agreement” in Section 6(a)(xii) is hereby deleted and replaced in its entirety with the following:

“...the Investment Advisory Agreement, between the Fund and the Adviser, dated January 31, 2018 (the “Investment Advisory Agreement”)...”

3.          Section 9(b) is hereby deleted and replaced in its entirety with the following:

(b)          On every date specified in Section 7(k)  hereof (including, without limitation, on every Request Date), Hunton Xxxxxxx Xxxxx LLP, counsel for the Agent, shall have furnished to the Agent a negative assurance letter, dated as of such date, and such counsel shall have received such papers and information as they may reasonably request to enable them to provide such letter.

4.          The notice address for Xxxxxxx Xxxxx LLP in Section 13 is hereby deleted and replaced in its entirety with the following:

“Hunton Xxxxxxx Xxxxx LLP 000 Xxxx Xxxxxx

Xxx Xxxx, Xxx Xxxx 00000 Attention: Xxxxxxx Xxxxxxxx”

5.          The notice address for Tortoise Energy Infrastructure Corporation in Section 13 is hereby deleted and replaced in its entirety with the following:

“Tortoise Energy Infrastructure Corporation 00000 Xxx Xxxxxx, Xxxxx 000 Xxxxxxx, Xxxxxx 00000 Attention:  P. Xxxxxxx Xxxxx”

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

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

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

9.          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:	/s/ P. Xxxxxxx Xxxxx
		Name:	P. Xxxxxxx Xxxxx
		Title:	Chief Executive Officer, Principal Financial Officer and Treasurer
	TORTOISE CAPITAL ADVISORS, L.L.C.
	By:	/s/ P. Xxxxxxx Xxxxx
		Name:	P. Xxxxxxx Xxxxx
		Title:	Managing Director
	ACCEPTED, as of the date first-above written:
	CANTOR XXXXXXXXXX & CO.
	By:	/s/ Xxxxxxx Xxxxx
		Name:	Xxxxxxx Xxxxx
		Title:	Senior Managing Director

Signature Page to Sixth Amendment to Tortoise Energy Infrastructure Corporation (TYG) Controlled Equity Offering^SM Sales Agreement