Theories of rationality advance principles that differ in topic, scope, and assumptions. A typical version of the principle of utility maximization formulates a standard rather than a procedure for decisions, evaluates decisions comprehensively, and relies on idealizations. I generalize the principle by removing some idealizations and making adjustments for their absence. The generalizations accommodate agents who have incomplete probability and utility assignments and are imperfectly rational. They also accommodate decision problems with unstable comparisons of options.