The present generation of X-ray telescopes emphasizes either high image quality (e.g. Chandra with sub-arc second resolution) or large effective area (e.g. XMM-Newton), while future observatories under consideration (e.g. Athena, AXSIO) aim to greatly enhance the effective area, while maintaining moderate (∼10 arc-seconds) image quality. To go beyond the limits of present and planned missions, the use of thin adjustable optics for the control of low-order figure error is needed to obtain the high image quality of precisely figured mirrors along with the large effective area of thin mirrors. The adjustable mirror prototypes under study at Smithsonian Astrophysical Observatory are based on two different principles and designs: 1) thin film lead-zirconate-titanate (PZT) piezoelectric actuators directly deposited on the mirror back surface, with the strain direction parallel to the glass surface (for sub-arc-second angular resolution and large effective area), and 2) conventional leadmagnesium- niobate (PMN) electrostrictive actuators with their strain direction perpendicular to the mirror surface (for 3-5 arc second resolution and moderate effective area). We have built and operated flat test mirrors of these adjustable optics. We present the comparison between theoretical influence functions as obtained by finite element analysis and the measured influence functions obtained from the two test configurations.