Single-cell genome sequencing methods are challenged by poor physical coverage and high error rates, making it difficult to distinguish real biological variants from technical artifacts. To address this problem, we developed a method called SNES that combines flow-sorting of single G1/0 or G2/M nuclei, time-limited multiple-displacement-amplification, exome capture, and next-generation sequencing to generate high coverage (96%) data from single human cells. We validated our method in a fibroblast cell line, and show low allelic dropout and false-positive error rates, resulting in high detection efficiencies for single nucleotide variants (92%) and indels (85%) in single cells.