Professional psychologists are often confronted with the task of making binary decisions about individuals, such as predictions about future behavior or employee selection. Test users familiar with linear models and Bayes's theorem are likely to assume that the accuracy of decisions is consistently improved by combination of outcomes across valid predictors. However, neither statistical method accurately estimates the increment in accuracy that results from use of additional predictors in the typical applied setting. It was demonstrated that the best single predictor often can perform better than do multiple predictors when the predictors are combined using methods common in applied settings. This conclusion is consistent with previous findings concerning G. Gigerenzer and D. Goldstein's (1996) "take the best" heuristic. Furthermore, the information needed to ensure an increment in fit over the best single predictor is rarely available. (Contains 5 tables, 2 figures, and 5 footnotes.)