Effective mapping strategies for quantitative trains must allow for the detection of the more important quantitative trait loci (QTLs) while minimizing false positives. Type I (false-positive) and Type II (false-negative) error rates were estimated from a computer simulation of QTL mapping in the BXD recombinant inbred (RI) set compromising 26 strains of mice, and comparisons made with theoretical predictions. The results are generally applicable to other RI sets when corrections are made for differing strain numbers and marker densities. Regardless of the number or magnitude of simulated QTLs contributing to the trait variance, the p value necessary to provide adequate protection against both Type I (alpha=.0001) and Type II (beta=.2) errors, a QTL would have to account for more than half of the between-strain (genetic) variance if the BXD or similar set was used alone. In contrast, a two-step mapping strategy was also considered, where RI strains are used as a preliminary screen for QTLs to be specifically tested (confirmed) in an F2 (or other) population. In this case, QTLs accounting for approximately 16% of the between-strain variance could be detected with an 80% probability in the BXD set when alpha = 0.2. To balance the competing goals of minimizing Type I and II errors, an economical strategy is to adopt a more stringent alpha initially for the RI screen, since this requires only a limited genome search in the F2 of the RI-implicated regions (approximately 10% of the F2 genome when p < .01 in the RIs). If confirmed QTLs do not account in the aggregate for a sufficient proportion of the genetic variance, then a more relaxed alpha value can be used in the RI screen to increase the statistical power. This flexibility in setting RI alpha values is appropriate only when adequate protection against Type I errors comes from the F2 (or other) confirmation test(s).