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This paper reports results on effective piezoelectric properties of advanced composites based on polydomain relaxor-ferroelectric single crystals of 0.67Pb(Mg1/3Nb2/3)O3 - 0.33PbTiO3. Two variants of the single crystal/porous polymer composite with 0-3-0 connectivity are proposed to study the role of microstructural factors in forming high piezoelectric sensitivity. The effective properties of the related 0-3 single crystal/polymer composite are predicted and considered to show ways of increasing the piezoelectric anisotropy and sensitivity. Examples of the volume-fraction and aspect-ratio dependences of the effective piezoelectric coefficients d3j*, g3j*, the hydrostatic piezoelectric coefficient gh*, and squared figures of merit d33* g33* and dh* gh* of composites are analysed to show in which ranges high piezoelectric sensitivity is attained. The presence of single-crystal polydomain inclusions in the porous 3-0 matrix promotes the large effective parameters (g33* ∼ 103 mV · m/N, gh* ∼ 103 mV · m/N, d33* g33* ∼ 10-10 Pa-1, and dh* gh* ∼ 10-10 Pa-1), and the obvious high-performance advantage of the 0-3-0 composites is discussed taking into account features of their microstructure. [ABSTRACT FROM AUTHOR]