The piezoelectric response of strained heterostructures and superlattices is examined. A general crystallographic direction of growth is assumed for a subcritical cubic piezoelectric layer. Piezoelectric fields appear only along (or opposite to) the growth axis, provided all three direction cosines of the latter, relative to the cubic axes, are nonzero. The formulation is based on elasticity theory, and the results are compared with other approaches in the literature. Standard and less standard directions of growth are worked out explicitly.