Genetic material sequenced from ancient samples is revolutionizing our understanding of the recent evolutionary past. However, ancient DNA is often degraded, resulting in low coverage, error-prone sequencing. Several solutions exist to this problem, ranging from simple approach such as selecting a read at random for each site to more complicated approaches involving genotype likelihoods. In this work, we present a novel method for assessing the relationship of an ancient sample with a modern population while accounting for sequencing error by analyzing raw read from multiple ancient individuals simultaneously. We show that when analyzing SNP data, it is better to sequencing more ancient samples to low coverage: two samples sequenced to 0.5x coverage provide better resolution than a single sample sequenced to 2x coverage. We also examined the power to detect whether an ancient sample is directly ancestral to a modern population, finding that with even a few high coverage individuals, even ancient samples that are very slightly diverged from the modern population can be detected with ease. When we applied our approach to European samples, we found that no ancient samples represent direct ancestors of modern Europeans. We also found that, as shown previously, the most ancient Europeans appear to have had the smallest effective population sizes, indicating a role for agriculture in modern population growth.