Phase diverse speckle (PDS) imaging is based on the use of multiple channels of raw image data, each independently encoded with a known pupil phase, that constrain a well designed image restoration algorithm to converge to a high-quality image even in the presence of noise. Fisher information furnishes a useful metric to assess the information added by each image channel to that already present in the others, and thus to arrive at a design-optimization procedure for choosing the best pupil phases. A combination of analytical and numerical/simulational results for a conventional two-channel PDS system operating under heavy turbulence will be presented to illustrate this powerful information-based optimization approach.