Abstract Small deviations from optimizing behavior can have substantial effects on economic equilibria. This paper analyzes deviations from optimization in consumer demand. We show how a measure of the Slutsky asymmetry of a demand function is related to the rate at which real income can rise along a smooth revealed preference cycle. We also relate the Slutsky asymmetry measure to the minimum distance between the given demand function and a function that is derivable from utility maximization. The results yield simple quantitative revealed preference interpretations for violations of Slutsky symmetry while suggesting how to compare the sizes of revealed preference inconsistencies.