Snapshot compressive imaging aims to capture high resolution images using low resolution detectors. The challenge is the generation of simultaneous optical projections that fulfil the compressed sensing reconstruction requirements. We propose the use of controlled aberrations through wavefront coding to produce point spread functions that can simultaneously code and multiplex the scene in a variety of ways. Apart from light efficiency, we can analytically characterize the system matrix response. We explore combinations of Zernike modes and analyze the corresponding coherence parameter. Simulation results using natively sparse and natural scenes demonstrate the feasibility of using controlled aberrations for compressive imaging.