In visual search, improved performance when a target appears at a recently cued location is taken as strong evidence that attention was shifted to this cue. Here, we provide evidence challenging the canonical interpretation of spatial-cueing (or cue-validity) effects and supporting the Priority Accumulation Framework (PAF). According to PAF, attentional priority accumulates over time at each location until the search context triggers selection of the highest-priority location. Spatial-cueing effects reflect how long it takes to resolve the competition and can thus be observed even when attention was never shifted to the cue. Here, we used a spatial-cueing paradigm with abruptly onset cues and search displays varying in target-distractor similarity. We show search performance on valid-cue trials deteriorated the more difficult the search, a finding that is incompatible with the standard interpretation of spatial-cueing effects. By using brief displays (Experiment 1) and by examining the effect of search difficulty on the fastest trials (Experiment 2), we invalidate alternative accounts invoking post-perceptual verification processes (Experiment 1) or occasional failures of the onset cue to capture attention (Experiment 2). In Experiment 3, we used a combination of the spatial-cueing and dot-probe paradigms. We show that the events that occurred in both the cue and search displays affected attentional distribution, and that the relative attentional priority weight that accumulated at the target location determined how easily the competition was resolved. These findings fully support PAF’s predictions.