Most "tests of neutrality" assess whether particular data sets depart from the predictions of a standard neutral model with no recombination. For Drosophila, where nuclear polymorphism data routinely show evidence of genetic exchange, the assumption of no recombination is often unrealistic. In addition, while conservative, this assumption is made at the cost of a great loss in power. Perhaps as a result, tests of the frequency spectrum based on zero recombination suggest an adequate fit of Drosophila polymorphism data to the predictions of the standard neutral model. Here, we analyze the frequency spectrum of a large number of loci in Drosophila melanogaster and D. simulans using two summary statistics. We use an estimate of the population recombination rate based on a laboratory estimate of the rate of crossing over per physical length and an estimate of the species' effective population size. In contrast to previous studies, we find that roughly half of the loci depart from the predictions of the standard neutral model. The extent of the departure depends on the exact recombination rate, but the global pattern that emerges is robust. Interestingly, these departures from neutral expectations are not unidirectional. The large variance in outcomes may be due to a complex demographic history and inconsistent sampling, or to the pervasive action of natural selection.