We study exact models for anisotropic gravitating stars with conformal symmetry. The gravitational potentials are related explicitly by the conformal vector. We use this relationship between the metric potentials to find new classes of exact solutions to the field equations. We identify a particular model to study the physical features and demonstrate that the model is well behaved. In particular the criteria for stability are satisfied. We regain masses, radii and surface redshifts for the compact objects PSR J1614-2230 and SAX J1808.4-3658.