Mask-dependent cuing effects, like those previously found in yes-no detection, were found in a task in which observers judged the orientations of orthogonally-oriented Gabor patches presented at cued or uncued locations. Attentional cues enhanced sensitivity for masked, but not unmasked, stimuli. Responses were faster to cued than to uncued stimuli, irrespective of masking. The distributions of response times and accuracy were well described by a diffusion process model of decision making. Mask-dependent cuing was explained by an orienting model in which: (a) decisions are based on stable stimulus representations in visual short term memory that determine the rate of evidence accumulation in the diffusion process; (b) inattention delays the entry of stimuli into short term memory, and (c) masks limit the visual persistence of stimuli.