We consider compressed sensing within a stochastic setting, where the signal or image of interest is drawn from a probability distribution that is in some sense compressible. Within this setting we consider some sample-distortion functions for i.i.d. compressible distributions and derive a simple sample distortion lower bound. We then extend the compressible model to consider a stochastic multi-resolution image model. Using empirical sample distortion functions we are able to compute an optimal bandwise sampling strategy and to accurately predict the compressed sensing possible performance gains available in compressive imaging.