High quality epitaxial layers (16) can be grown on a multi-layer substrate (10) which has a crystalline pseudomorphic layer (12) with an exposed surface used for the epitaxial growth. The pseudomorphic layer (12) of the substrate (10) has a thickness at or below the pseudomorphic limit so it will be deformed as stress forces are developed during epitaxial growth of heteroepitaxial structures. A plastically deformable layer (14) is bonded to the pseudomorphic layer (12). This plastically deformable layer (14) is made of material that plastically flows at epitaxial growth temperatures.