Congenic strains can now be constructed guided by the transmission of DNA markers. This allows not only selection for transmission of a desired, donor-derived differential region but also selection against the transmission of unwanted donor origin genomic material. The additional selection capacity should allow congenic strains to be produced in fewer generations than is possible with random backcrosses. Here, we consider modifications of a standard backcross breeding scheme to produce congenic mice by the inclusion of genotype-based selective breeding strategies. Simulation is used to evaluate the consequences of each strategy on the number of chromosomes that contain unwanted, donor-derived genetic material and the average length of this unwanted donor DNA for each backcross generation. Our prototypic strategy was to choose a single mouse to sire each generation using criteria designed to select against the transmission of chromosomes, other than the one containing the replacement genomic region, that contain any donor origin sequence at all. This chromosome elimination strategy resulted in an average of 16.4 chromosomes free of donor DNA in mice of the third backcross (N3) generation. A strategy based solely on positive selection for the replacement region required six backcross generations to achieve the same results.