CERTIFICATION PURSUANT TO RULE 30a-2(b) UNDER THE 1940 ACT AND SECTION 906 OF
                             THE SARBANES-OXLEY ACT

I, James A. Bowen, Chairman of the Board,  President and Chief Executive Officer
of First Trust Strategic High Income Fund III (the "Registrant"), certify that:

      1.    The Form N-CSR of the Registrant  (the "Report") fully complies with
            the  requirements  of  Section  13(a)  or  15(d)  of the  Securities
            Exchange Act of 1934, as amended; and

      2.    The  information  contained in the Report  fairly  presents,  in all
            material respects, the financial condition and results of operations
            of the Registrant.

Date: March 20, 2008       /s/ James A. Bowen
                           -----------------------------------------------------
                           James A. Bowen, Chairman of the Board,
                           President and Chief Executive Officer
                           (principal executive officer)

I, Mark R. Bradley,  Treasurer,  Controller,  Chief Financial  Officer and Chief
Accounting   Officer  of  First  Trust  Strategic  High  Income  Fund  III  (the
"Registrant"), certify that:

      1.    The Form N-CSR of the Registrant  (the "Report") fully complies with
            the  requirements  of  Section  13(a)  or  15(d)  of the  Securities
            Exchange Act of 1934, as amended; and

      2.    The  information  contained in the Report  fairly  presents,  in all
            material respects, the financial condition and results of operations
            of the Registrant.

Date: March 20, 2008       /s/ Mark R. Bradley
                           -----------------------------------------------------
                           Mark R. Bradley, Treasurer, Controller,
                           Chief Financial Officer and Chief
                           Accounting Officer
                           (principal financial officer)