In recent years, carbon fiber reinforced polymer CFRP mirrors been proposed for use in future imaging satellites. Compared to traditional glass-based mirrors, CFRP mirrors offer reduced manufacturing times, lower coefficients of thermal expansion, lower areal density, and higher strength-to-weight ratios. Shorter manufacturing times promise to reduce program schedule requirements and cost. These advantages come at the expense of surface quality, which results in wavefront errors that are outside of the diffraction limit for optical imaging. To compensate for the reduced surface quality of CFRP mirrors, a deformable mirror DM is required in the optical path. During this research, the surface quality of a CFRP mirror was evaluated to establish a root-mean-square RMS error threshold for the DM corrections. An integral DM control law that employed a constrained least-squares solution was utilized to reduce the overall system wavefront error to below the specified CFRP error threshold. The application of this control law yielded a 38 reduction in RMS wavefront error as compared to the CFRP error threshold, thus reducing the CFRP RMS surface performance requirements by the same amount. Reducing the surface performance requirements of CFRP mirrors is a critical step toward employing these mirrors in future imaging satellites.