Many pulse-echo imaging systems use focused beams to improve lateral resolution. The beam width is determined by the choice of source and apodization function, the frequency, and the physics of focusing. Postprocessing strategies to improve lateral resolution can be limited by the need for conditioning the mathematics of inverse filtering, due to instabilities. We present an analysis that defines key constraints on sampled versions of lateral beampatterns. Within these constraints are useful symmetric beampatterns, which, when properly sampled, can have a stable inverse filter. A framework for analysis and processing is described and applied to phantoms and tissues to demonstrate the improvements that can be realized.