We consider the problem of multicriteria decision making (MCDM) in the situation in which there exists a prioritization of criteria. A good example of prioritization among criteria occurs in the case of air travel, where concerns about passenger safety have a higher priority then economic concerns. Tradeoffs between saving on gasoline usage and jeopardizing passenger safety are unacceptable. We show how this prioritization of criteria can be modeled by using importance weights in which the weights associated with the lower priority criteria are related to the satisfaction of the higher priority criteria. We provide some models that allow for the formalization of these prioritized MCDM problems using both the Bellman-Zadeh paradigm for MCDM and the ordered weighted averaging (OWA) operator method.