Despite recent technological advances in DNA sequencing, incomplete coverage remains to be an issue in population genomics, in particular for studies that include ancient samples. Here, we describe an approach to estimate population divergence times for non-overlapping sequence data that is based on probabilities of different genealogical topologies under a structured coalescent model. We show that the approach can be adapted to accommodate common problems such as sequencing errors and postmortem nucleotide misincorporations, and we use simulations to investigate biases involved with estimating genealogical topologies from empirical data. The approach relies on three reference genomes and should be particularly useful for future analysis of genomic data that comprise of nonoverlapping sets of sequences, potentially from different points in time. We applied the method to shotgun sequence data from an ancient wolf together with extant dogs and wolves and found striking resemblance to previously described fine-scale population structure among dog breeds. When comparing modern dogs to four geographically distinct wolves, we find that the divergence time between dogs and an Indian wolf is smallest, followed by the divergence times to a Chinese wolf and a Spanish wolf, and a relatively long divergence time to an Alaskan wolf, suggesting that the origin of modern dogs is somewhere in Eurasia, potentially southern Asia. We find that less than two-thirds of all loci in the boxer and poodle genomes are more similar to each other than to a modern gray wolf and that--assuming complete isolation without gene flow--the divergence time between gray wolves and modern European dogs extends to 3,500 generations before the present, corresponding to approximately 10,000 years ago (95% confidence interval [CI]: 9,000-13,000). We explicitly study the effect of gene flow between dogs and wolves on our estimates and show that a low rate of gene flow is compatible with an even earlier domestication date ∼30,000 years ago (95% CI: 15,000-90,000). This observation is in agreement with recent archaeological findings and indicates that human behavior necessary for domestication of wild animals could have appeared much earlier than the development of agriculture.