Given the difficulties people experience in making trade-offs, what are the consequences of using simple models that avoid trade-offs? We examine choices by such models in environments where "true" preferences are linear and attributes are characterized by binary attributes. A deterministic elimination-by-aspects (DEBA) model is highly effective over a range of conditions. When preferences are quite compensatory, however, a modified equal weighting (EW) model that uses DEBA to resolve ties is more effective. We explore the sensitivity of results to errors in using DEBA, to different distributions of alternatives, and to error in "true" preferences. Under the conditions examined here, the outcomes of these "boundedly rational" models are highly consistent with "rational" models that explicitly confront trade-offs. We emphasize the importance of binary attributes in reaching these conclusions.