We present full-genome genotype imputations for 100 classical laboratory mouse strains, using a novel method. Using genotypes at 549,683 SNP loci obtained with the Mouse Diversity Array, we partitioned the genome of 100 mouse strains into 40,647 intervals that exhibit no evidence of historical recombination. For each of these intervals we inferred a local phylogenetic tree. We combined these data with 12 million loci with sequence variations recently discovered by whole-genome sequencing in a common subset of 12 classical laboratory strains. For each phylogenetic tree we identified strains sharing a leaf node with one or more of the sequenced strains. We then imputed high- and medium-confidence genotypes for each of 88 nonsequenced genomes. Among inbred strains, we imputed 92% of SNPs genome-wide, with 71% in high-confidence regions. Our method produced 977 million new genotypes with an estimated per-SNP error rate of 0.083% in high-confidence regions and 0.37% genome-wide. Our analysis identified which of the 88 nonsequenced strains would be the most informative for improving full-genome imputation, as well as which additional strain sequences will reveal more new genetic variants. Imputed sequences and quality scores can be downloaded and visualized online.