We demonstrate a versatile thin lensless camera with a designed phase-mask placed at sub-2 mm from an imaging CMOS sensor. Using wave optics and phase retrieval methods, we present a general-purpose framework to create phase-masks that achieve desired sharp point-spread-functions (PSFs) for desired camera thicknesses. From a single 2D encoded measurement, we show the reconstruction of high-resolution 2D images, computational refocusing, and 3D imaging. This ability is made possible by our proposed high-performance contour-based PSF. The heuristic contour-based PSF is designed using concepts in signal processing to achieve maximal information transfer to a bit-depth limited sensor. Due to the efficient coding, we can use fast linear methods for high-quality image reconstructions and switch to iterative nonlinear methods for higher fidelity reconstructions and 3D imaging.