Across saccades, small displacements of a visual target are harder to detect and their directions more difficult to discriminate than during steady fixation. Prominent theories of this effect, known as saccadic suppression of displacement, propose that it is due to a bias to assume object stability across saccades. Recent studies comparing the saccadic effect to masking effects suggest that suppression of displacement is not saccade-specific. Further evidence for this account is presented from two experiments where participants judged the size of displacements on a continuous scale in saccade and mask conditions, with and without blanking. Saccades and masks both reduced the proportion of correctly perceived displacements and increased the proportion of missed displacements. Blanking improved performance in both conditions by reducing the proportion of missed displacements. Thus, if suppression of displacement reflects a bias for stability, it is not a saccade-specific bias, but a more general stability assumption revealed under conditions of impoverished vision. Specifically, I discuss the potentially decisive role of motion or other transient signals for displacement perception. Without transients or motion, the quality of relative position signals is poor, and saccadic and mask-induced suppression of displacement reflects performance when the decision has to be made on these signals alone. Blanking may improve those position signals by providing a transient onset or a longer time to encode the pre-saccadic target position.