Bonded, thin film compliant substrates can be used to reduce the strain in a lattice-mismatched overlayer during epitaxial growth. We have presented an initial demonstration of the use of thin film GaAs compliant substrates fabricated by epitaxial liftoff or substrates removal and bonded to a mechanical host. This processing approach can be coupled with the patterning of the bended surface to realize a lateral thickness variation. This thickness variation, in turn, can be used to realize a lateral strain variation in the growing mismatched overlayer. The strain can then be used to modify molecular beam epitaxy (MBE) growth kinetics, such as cation desorption and migration. With this technique the lateral control of composition and thickness can be realized without any surface topography. In this article, we discuss the growth of InGaAs films on compliant substrates produced by epitaxial lift-off and substrate removal. In addition, we discuss the various extrinsic effects associated with the compliant substrates, including the effects of the bonding and the results of MBE temperature cycling experiments. Finally, the characteristics of InGaAs thin films grown on GaAs patterned compliant substrates are presented.