Klunk et al. analyzed ancient DNA data from individuals in London and Denmark before, during and after the Black Death [1], and argued that allele frequency changes at immune genes were too large to be produced by random genetic drift and thus must reflect natural selection. They also identified four specific variants that they claimed show evidence of selection including at ERAP2, for which they estimate a selection coefficient of 0.39-several times larger than any selection coefficient on a common human variant reported to date. Here we show that these claims are unsupported for four reasons. First, the signal of enrichment of large allele frequency changes in immune genes comparing people in London before and after the Black Death disappears after an appropriate randomization test is carried out: the P value increases by ten orders of magnitude and is no longer significant. Second, a technical error in the estimation of allele frequencies means that none of the four originally reported loci actually pass the filtering thresholds. Third, the filtering thresholds do not adequately correct for multiple testing. Finally, in the case of the ERAP2 variant rs2549794, which Klunk et al. show experimentally may be associated with a host interaction with Y. pestis, we find no evidence of significant frequency change either in the data that Klunk et al. report, or in published data spanning 2,000 years. While it remains plausible that immune genes were subject to natural selection during the Black Death, the magnitude of this selection and which specific genes may have been affected remains unknown.