We introduce the first general test of capacity-constrained learning models. Cognitive economic models of this type share the common feature that constraints on perception are exogenously fixed, as in the widely used fixed-capacity versions of rational inattention (Sims 2003) and efficient coding (Woodford 2012). We show that choice data are consistent with capacity-constrained learning if and only if they satisfy a No Improving (Action or Attention) Switches (NIS) condition. Based on existing experiments in which the incentives for being correct are varied, we find strong evidence that participants fail NIS for a wide range of standard perceptual tasks: identifying the proportion of ball colors, recognizing shapes, and counting the number of balls. However, we find that this is not true for all existing perceptual tasks in the literature, which offers insights into settings where we do or do not expect incentives to impact the extent of attention.