The transverse piezoelectric coefficient d31⋆ has been calculated for the six domain-engineered structures occurring in perovskite single crystals, using data for rhombohedral PMN-33PT [0.67Pb(Mg1∕3Nb2∕3)O3-0.33PbTiO3], orthorhombic potassium niobate (KNbO3), tetragonal barium titanate (BaTiO3), and tetragonal lead titanate (PbTiO3). Unlike the longitudinal coefficient (d33⋆), d31⋆ is found to be strongly dependent on the transverse (x1′) direction of the as-cut crystal. In general, different domains in a domain-engineered structure will contribute different values of d31⋆ to that measured. Predicting the global d31⋆ is therefore difficult since it will depend on the proportion of each domain variant in the structure. Important qualitative differences between tetragonal BaTiO3 and PbTiO3 are discussed. Whereas polarization rotation is important in BaTiO3, PbTiO3 shows a stronger collinear piezoelectric effect due the absence of a low-temperature ferroelectric-ferroelectric phase transition. This leads to low values of d33⋆ and even positive values of d31⋆ in the [111]C-poled (C: pseudocubic) domain-engineered structure. The methodology described can be usefully applied to all perovskites.