A novel parallel-connected 2–2 single-domain 0.67Pb(Mg1/3Nb2/3)O3 – 0.33PbTiO3 crystal / polymer composite with various orientations of polarization vectors of the components is proposed to analyze behavior of electromechanical coupling factors k*3j and k*k where j = 1, 2 and 3. It is shown that the combination of the highly piezo-active relaxor-ferroelectric single-domain component and the piezoelectric polymer provides considerable values of k*k (min k*k » –0.8 and max k*k» 0.7) and |k*33| (about 0.9). The active role of the polarization orientation effect and the composite structure in attaining the high performance is emphasized in this work. A strong correlation between k*k and the hydrostatic piezoelectric coefficient is first revealed near min k*k and max k*k of the 2–2 composite. Some advantages concerned with the presence of the single-domain component in the 2–2 composite are discussed in connection with the large values of k*3j and k*k as well as with the considerable anisotropy of k*3j.