EXHIBIT 12(B)

    CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Joseph F. Murphy, President and Chief Executive Officer and Steven M. Anderson,
Treasurer and Chief Financial Officer of Mellon Optima L/S Strategy Fund, LLC
(the "Registrant"), each certify to the best of their knowledge that:

1.   The Registrant's periodic report on Form N-CSR for the period ended March
     31, 2009 (the "Form N-CSR") fully complies with the requirements of Section
     15(d) of the Securities Exchange Act of 1934, as amended; and

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


/s/ JOSEPH F. MURPHY
- -------------------------------------
Joseph F. Murphy
President and Chief Executive Officer

Date: June 9, 2009


/s/ STEVEN M. ANDERSON
- -------------------------------------
Steven M. Anderson
Treasurer and Chief Financial Officer

Date: June 9, 2009

A signed original of this written statement required by Rule 30a-216, under the
Investment Company Act of 1940 and 18 U.S.C. Section 1350 will be retained by
the Registrant and furnished to the Securities and Exchange Commission or its
staff upon request.

This certification is being furnished to the Securities and Exchange Commission
solely pursuant to Rule 30a-2(b) under the Investment Company Act of 1940, as
amended, and 18 U.S.C. Section 1350 and is not being filed as part of the Form
N-CSR with the Commission.