Genome-wide nucleotide variation in non-African populations of Drosophila melanogaster is a subset of variation found in East sub-Saharan African populations, suggesting a bottleneck in the history of the former. We implement an approximate Bayesian approach to infer the timing, duration, and severity of this putative bottleneck and ask whether this inferred model is sufficient to account for patterns of variability observed at 115 loci scattered across the X chromosome. We estimate a recent bottleneck 0.006N(e) generations ago, somewhat further in the past than suggested by biogeographical evidence. Using various proposed statistical tests, we find that this bottleneck model is able to predict the majority of observed features of diversity and linkage disequilibrium in the data. Thus, while precise estimates of bottleneck parameters (like inferences of selection) are sensitive to model assumptions, our results imply that it may be unnecessary to invoke frequent selective sweeps associated with the dispersal of D. melanogaster from Africa to explain patterns of variability in non-African populations.