Two effects of the matrix subsystem on the piezoelectric performance and hydrostatic parameters are first studied in novel 1–0–3 composites that contain relaxor-ferroelectric single-crystal rods surrounded by a ferroelectric ceramic/ polymer matrix with 0–3 connectivity. First, the influence of the mutual orientation of the poling direction of the single-crystal and ceramic components on the properties of the 1–0–3 composite is discussed to demonstrate advantages concerned with the high hydrostatic piezoelectric performance and large anisotropy of squared figures of merit. In a 1–0–3 0.67Pb(Mg1/3Nb2/3)O3 − 0.33PbTiO3 single crystal/ (Pb1–xCax)TiO3 ceramic/araldite composite with x = 0.20–0.25, values of max g_ h * 102 mV · m/N and max(d_ hg_ h) * 10−11 Pa−1 are achieved at specific volume-fraction and rotation-angle ranges due to the new orientation effect in the presence of a highly anisotropic 0–3 matrix. Second, the influence of the aspect ratio of ceramic inclusions on the piezoelectric and hydrostatic parameters of the 1– 0–3 composite based on relaxor-ferroelectric SCs is studied. In this case, the elastic anisotropy of the 0–3 matrix plays the key role in forming the large effective parameters of the composite. The studied composites can be used in piezoelectric sensor, energy-harvesting and hydrophone applications.