A composite containing Lead Zirconate Titanate (PZT)-type ferroelectric and corundum ceramics is studied as a material with a combination of a relatively high piezoelectric activity, significant piezoelectric anisotropy and a large mechanical quality factor. Experimental data on four piezoelectric coefficients d(43)(star), e(43)(star), g(33)(star), and h(33)(star) are first analysed for a composite with almost equal volume fractions of corundum inclusions m(c), and air pores my. The presence of both corundum inclusions and air pores of similar volume fractions in the composite strongly influences relationships between its piezoelectric coefficients and quality factors. Maxima of g(33)(star) and h(33)(star), electromechanical coupling factor k(t)(star): and resonator figure of merit M-star are observed in a narrow me range (0.09< m(c) < 0.14), and this has no analogs among other piezo-active composites with two ceramic components. New experimental results on the piezoelectric performance are interpreted in terms of a microstructural model whereby the electromechanical interaction between the ferroelectric ceramic/corundum regions in the porous ferroelectric ceramic medium (either poled or non-poled) plays an important role. The studied composite is of interest as an active element of piezoelectric sensors and other piezotechnical transducer devices.