First Trust Exchange-Traded AlphaDEX(R) Fund
                       120 East Liberty Drive, Suite 400
                            Wheaton, Illinois 60187


                                  May 9, 2011


Securities and Exchange Commission
100 F Street, N.E.
Washington, DC 20549



      Re:      First Trust Mega Cap AlphaDEX(R) Fund (the "Fund")


Ladies and Gentlemen:

      The undersigned, First Trust Exchange-Traded AlphaDEX(R) Fund (the
"Registrant") and First Trust Portfolios L.P., the principal underwriter of the
Funds, pursuant to the provisions of Rule 461 of the General Rules and
Conditions of the Securities and Exchange Commission (the "Commission") under
the Securities Act of 1933, as amended, hereby respectfully request that the
Commission grant acceleration of the effectiveness of Post-Effective Amendment
No. 15 to the Registrant's Registration Statement on Form N-1A (Registration No.
333-140895), filed on May 9, 2011, so that the same may become effective at
3:00 p.m., Eastern Time on May 10, 2011, or as soon thereafter as practicable.

                                   Very truly yours,

                                   First Trust Exchange-Traded AlphaDEX(R) Fund


                                   By:  /s/ W. Scott Jardine
                                       ------------------------------------
                                           W. Scott Jardine, Secretary


                                   First Trust Portfolios L.P.


                                   By:  /s/ W. Scott Jardine
                                       ------------------------------------
                                           W. Scott Jardine, Secretary