FIRST AMENDMENT TO TORTOISE ENERGY CAPITAL CORPORATION COMMON STOCK ($0.001 PAR VALUE) CONTROLLED EQUITY OFFERINGSM SALES AGREEMENT

Exhibit h.10
Execution Version

FIRST AMENDMENT TO

TORTOISE ENERGY CAPITAL CORPORATION
COMMON STOCK ($0.001 PAR VALUE)

SALES AGREEMENT

     THIS AMENDMENT TO (the “Amendment”) the Controlled Equity Offering Sales Agreement^SM dated as of August 3, 2009 (the “Sales Agreement”) is made and entered into effective as of April 21, 2010, by and between Tortoise Energy Capital Corporation, a Maryland corporation (the “Fund”), the Fund’s investment adviser, Tortoise Capital Advisors, LLC, a Delaware limited liability company (the “Adviser”), and Cantor ▇▇▇▇▇▇▇▇▇▇ & Co. (“CF&Co.”).

     WHEREAS, the Fund and the Adviser have amended the Investment Advisory Agreement and the Stock Transfer Agency Agreement (as defined in the Sales Agreement); and

     WHEREAS, the Fund and the Adviser have determined that it would be in the best interest of the Company to amend the definition of “Fund Agreements” so that such term refers to the amended Investment Advisory Agreement and the Stock Transfer Agency Agreement;

     NOW THEREFORE, in consideration of the mutual covenants and agreements contained herein, the parties agree as follows:

     1. Section 6(a)(xii) of the Sales Agreement is hereby deleted in its entirety and the following should be added in its place:

Absence of Defaults and Conflicts. The Fund is not (i) in violation of its charter or by-laws, or (ii) in default in the performance or observance of any obligation, agreement, covenant or condition contained in any contract, indenture, mortgage, deed of trust, loan or credit agreement, note, lease or other agreement or instrument to which it is a party or by which it may be bound, or to which any of the property or assets of the Fund is subject (collectively, “Agreements and Instruments”) except, with respect to this clause (ii), for such violations or defaults that would not result in a Material Adverse Effect; and the execution, delivery and performance of this Agreement, and the Alternative Distribution Agreement, and the consummation of the transactions contemplated in this Agreement and the Alternative Distribution Agreement and in the Registration Statement (including the issuance and sale of the Shares and the use of the proceeds from the sale of the Shares as described in the General Disclosure Package and the Prospectus under the caption “Use of Proceeds”) and compliance by the Fund with its obligations thereunder have been duly authorized by all necessary corporate action and do not and will not, whether with or without the giving of notice or passage of time or both, conflict with or constitute a breach of, or default or Repayment Event (as defined below) under, or result in the creation or imposition of any lien, charge or encumbrance upon any property or assets of the Fund pursuant to, the Investment Advisory Agreement, between the Fund and the Adviser, dated September 15, 2009 (the “Investment Advisory Agreement”), the Custody Agreement, between the Fund and U.S. Bank National Association, dated May

25, 2005 (the “Custody Agreement”), the Stock Transfer Agency Agreement, between the Fund and Computershare Investor Services, LLC, dated May 10, 2005, as amended by that certain addendum thereto between the same parties dated as of November 20, 2009 (the “Stock Transfer Agency Agreement”), the Fund Administration Servicing Agreement, between the Fund and U.S. Bancorp Fund Services, LLC, dated May 25, 2005, as amended by that certain addendum thereto between the same parties dated as of October 24, 2007 (the “Fund Administration Servicing Agreement”) and the Fund Accounting Servicing Agreement, between the Fund and U.S. Bancorp Fund Services, LLC, dated September 5, 2006 (the “Fund Accounting Servicing Agreement”, and collectively with the Investment Advisory Agreement, Custody Agreement, Stock Transfer Agency Agreement and the Fund Administration Servicing Agreement, the “Fund Agreements”) and the Agreements and Instruments (except for such conflicts, breaches or defaults or liens, charges or encumbrances that would not result in a Material Adverse Effect), nor will such action result in any violation of the provisions of the charter or by-laws of the Fund or any applicable law, statute, rule, regulation, judgment, order, writ or decree of any government, government instrumentality or court, domestic or foreign, having jurisdiction over the Fund or any of its assets, properties or operations (except for such violations that would not result in a Material Adverse Effect). As used herein, a “Repayment Event” means any event or condition which gives the holder of any note, debenture or other evidence of indebtedness (or any person acting on such holder’s behalf) the right to require the repurchase, redemption or repayment of all or a portion of such indebtedness by the Fund.

     2. Unless otherwise defined herein, all capitalized terms used in this Amendment shall have the same meanings as set forth in the Sales Agreement.

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

     4. 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, this Amendment is executed this 21st day of April, 2010.