We re-examine the evidence behind the controversial hypothesis that syphilis epidemics cycle. We used the same methods (spectral analysis) used by the proponents of this hypothesis to reanalyse a longitudinal dataset provided by the US Centers for Disease Control and Prevention (CDC). We also analysed a longitudinal CDC mortality dataset. To investigate the theoretical results generated by the transmission model that was used to support the hypothesis, we simulated the model and predicted the expected dynamics of syphilis epidemics. By contrast with previous findings, we found that neither of the CDC's datasets provides compelling evidence that syphilis epidemics cycle, and the transmission model (if more reasonable parameter values are used) does not predict cycling behaviour. We explain the possible reasons for the previous proposal that syphilis epidemics cycle. Our findings imply that it is quite possible that the CDC could be successful in eliminating syphilis within the next few decades.