We study orbits in simplified models of galaxies which consist of two components, a disk and a halo. The disk is idealized as razor-thin, though we present evidence that this simplifying assumption is not critical. We find that the presence of the disk causes many more resonances than have been found in similar smooth potentials. Those resonances grow at relatively modest values of energy, overlap, and give rise to many stochastic orbits. A significant range of regular orbits remain and show smooth KAM curves, even though the discontinuous potential due to the razor-thin disk means that current versions of the KAM theorem do not apply.