Selective attention is a most intensively studied psychological phenomenon, rife with theoretical suggestions and schisms. A critical idea is that of limited capacity, the allocation of which has produced half a century's worth of conflict about such phenomena as early and late selection. An influential resolution of this debate is based on the notion of perceptual load (Lavie, 2005, TICS, 9: 75), which suggests that low-load, easy tasks, because they underuse the total capacity of attention, mandatorily lead to the processing of stimuli that are irrelevant to the current attentional set; whereas high-load, difficult tasks grab all resources for themselves, leaving distractors high and dry. We argue that this theory presents a challenge to Bayesian theories of attention, and suggest an alternative, statistical, account of key supporting data.