Several phase-modulation functions have been reported to decrease the aberration variance of the modulation-transfer-function (MTF) in aberration-tolerant hybrid imaging systems. The choice of this phase-modulation function is crucial for optimization of the overall system performance. To prevent a significant loss in signal-to-noise ratio, it is common to enforce restorability constraints on the MTF, requiring trade of aberration-tolerance and noise-gain. Instead of optimizing specific MTF characteristics, we directly minimize the expected imaging-error of the joint design. This method is used to compare commonly used phase-modulation functions: the antisymmetric generalized cubic polynomial and fourthdegree rotational symmetric phase-modulation. The analysis shows how optimal imaging performance is obtained using moderate phase-modulation, and more importantly, the relative merits of the above functions. © 2010 Optical Society of America.