A chromosome substitution strain (CSS) is an inbred strain in which one chromosome has been substituted from a different inbred strain by repeated backcrossing. A complete CSS set has one strain representing each chromosome against a uniform background, thus allowing genome-wide scans to be carried out for quantitative trait loci (QTLs) influencing any trait of interest. A one-way ANOVA by strain is first carried out, followed by planned comparisons using Dunnett's method. A QTL is detected and mapped to a chromosome when a significant difference is observed in a background strain vs CSS comparison. The most efficient ratio of background to CSS mice in any one comparison is 4.5:1, and the threshold for p <.05 genome-wide significance is estimated to be p =.003 to.004, a much less stringent criterion than any other mammalian mapping population. The use of false discovery rates tends to further reduce threshold stringency. Comparisons are made to the widely used conventional F(2) intercross, and both advantages and disadvantages are noted. The proportion of the trait variance due to a QTL is often much larger than the same QTL in an F(2), and the number of generations to attain fine mapping is greatly reduced. To serve as guidelines for planning experiments, methods to estimate sample sizes for QTL detection are presented for the initial genome scan and for subsequent fine mapping.