Individuals face nonlinear incentives in myriad situations. We test a fundamental assumption in such settings: that individuals display stable preferences when facing linear and nonlinear incentives. We use a laboratory experiment to characterize how revealed preferences are affected by changes in the budget set environment. Choices under kinked budgets exhibit the same very high levels of internally consistent behavior as they do under linear budgets. However, for about half the subjects, choices across settings are inconsistent with the maximization of a stable preference. Subjects displaying arbitrary consistency exhibit large and significant changes in utility parameters, risk premiums, and price elasticities across settings.