Single-cell genomics is critical for understanding cellular heterogeneity in cancer, but existing library preparation methods are expensive, require sample preamplification and introduce coverage bias. Here we describe direct library preparation (DLP), a robust, scalable, and high-fidelity method that uses nanoliter-volume transposition reactions for single-cell whole-genome library preparation without preamplification. We examined 782 cells from cell lines and triple-negative breast xenograft tumors. Low-depth sequencing, compared with existing methods, revealed greater coverage uniformity and more reliable detection of copy-number alterations. Using phylogenetic analysis, we found minor xenograft subpopulations that were undetectable by bulk sequencing, as well as dynamic clonal expansion and diversification between passages. Merging single-cell genomes in silico, we generated 'bulk-equivalent' genomes with high depth and uniform coverage. Thus, low-depth sequencing of DLP libraries may provide an attractive replacement for conventional bulk sequencing methods, permitting analysis of copy number at the cell level and of other genomic variants at the population level.