Effective piezoelectric coefficients e33*, d 33*, g33*, and h33*, squared figures of merit d33* g33* and d h* gh*, and other related parameters of novel 0-3 and 0-3-0 composites based on single crystals of relaxor-ferroelectric solid solutions of (1.x)Pb(Mg1/3Nb2/3)O3-xPbTiO 3 are studied using the effective field method, effective medium method and finite element method. The volume-fraction dependences of a number of parameters and figures of merit are determined using the above methods and compared for composites with aligned prolate spheroidal inclusions. Four parameter ratios that determine interconnections between the effective electromechanical constants of the 0-3-type composites are first introduced. These parameter ratios are used to interpret the longitudinal dielectric and piezoelectric response of composite structures with prolate inclusions that exhibit high piezoelectric activity. The role of piezoelectric anisotropy and activity of the composite components in forming the longitudinal piezoelectric effect is analysed. Specific novel composite architectures with high piezoelectric sensitivity (longitudinal and hydrostatic) are identified and discussed.