Pendry’s perfect lens has spurred intense interest for its practical realization at visible frequencies. However, fabrication of low-loss isotropic left-handed metamaterials is a current challenge. In this work, we theoretically show that under specific conditions anisotropic metamaterial slabs can emulate Pendry’s perfect-lens phenomenon on a plane. Geometric optics leads to a new lens formula for this special anisotropic metamaterial superlens, which allows significant shrinkage of the metamaterial slab thickness for a certain range of far-field operation. Conversely, such anisotropic metamaterial superlens with the same thickness as its isotropic analog can operate for much larger distances between object and lens. We present numerical simulations which confirm our theoretical calculations. In particular, we find subdiffraction focusing that rivals the perfect isotropic negative-index metamaterial lens performance and obeys the new lens formula as predicted. In addition, we demonstrate that it is possible to attain far-field superfocusing with a metamaterial slab as thin as half the free-space wavelength. We believe this work will inspire new anisotropic metamaterial designs and opens a promising route for the realization of compact far-field superlenses in the visible regime.