For efficient storage and transmission of stereoscopic images over bandwidth-limited channels, compression can be achieved by degrading 1 monocular input of a stereo pair and maintaining the other at the desired quality. The desired quality of the fused stereoscopic image can be achieved, provided that binocular vision assigns greater weight to the nondegraded input. A psychophysical matching procedure was used to determine if such over-weighting occurred when the monocular degradation included blur or blocking artifacts. Over-weighting of the nondegraded input occurred for blur, but under-weighting of the nondegraded input occurred for blockiness. Some participants exhibited ocular dominance, but this did not affect the blur results. The authors conclude that blur, but not blockiness, is an acceptable form of monocular degradation.