The effectiveness of decision rules depends on characteristics of both rules and environments. A theoretical analysis of environments specifies the relative predictive accuracies of the lexicographic rule 'take-the-best' (TTB) and other simple strategies for binary choice. We identify three factors: how the environment weights variables; characteristics of choice sets; and error. For cases involving from three to five binary cues, TTB is effective across many environments. However, hybrids of equal weights (EW) and TTB models are more effective as environments become more compensatory. In the presence of error, TTB and similar models do not predict much better than a naïve model that exploits dominance. We emphasize psychological implications and the need for more complete theories of the environment that include the role of error.