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 26, 2009                       /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 26, 2009                       /s/ Mark R. Bradley
                                           -------------------------------------
                                           Mark R. Bradley, Treasurer,
                                           Controller, Chief Financial Officer
                                           and Chief Accounting Officer
                                           (principal financial officer)