We present a model in which supersymmetry is dynamically broken at comparatively low energies. Previous efforts to construct simple models of this sort have been hampered by the presence of axions. The present model, which exploits an observation of Bagger, Poppitz and Randall to avoid this problem, is far simpler than previous constructions. Models of this kind do not suffer from the naturalness difficulties of conventional supergravity models, and make quite definite predictions for physics over a range of scales from 100's of GeV to 1000's of TeV. Thus ``Renormalizable Visible Sector Models'' are a viable alternative to more conventional approaches. Our approach also yields a viable example of hidden sector dynamical supersymmetry breaking.