We optimize InAsyP1-y buffer layers and compositional grades for lattice-mismatched heteroepitaxy of GaxIn1-xAs/InAsyP1-y double-heterostructures on InP. The strains of the active and buffer layers depend on the bulk misfit difference between these layers. The misfit difference is adjusted to eliminate strain in the active layer, thus avoiding misfit dislocations and surface topography that would otherwise form to relieve strain. The optimized structure uses an "overshoot" with respect to the conventional design in the misfit and As composition of the InAsyP1-y buffer. Nearly optimized heterostructures typically show excellent structural quality and extended minority-carrier lifetimes. (C) 2007 Elsevier B.V. All rights reserved.