We investigate the long-period source spectra of oceanic transform earthquakes and find that previously proposed slow rupture components can be explained as artifacts generated by the modeling procedure. We use low-frequency (≤20 mHz) Rayleigh and Love waves to calculate the amplitude spectra of five earthquakes on the Romanche and Chain transform faults in the equatorial mid-Atlantic Ocean. We find that errors and approximations in the centroid depth, focal mechanism, and earth structure at the source have significant effects on the shape of the source spectra. If global catalog values and an average crustal model are assumed, the spectra exhibit apparent anomalous energy at long periods which has previously been interpreted as a result of slow rupture. We recalculate the source spectra using precise, independently determined depths and moment tensors and a more realistic oceanic crustal structure in the source region. The resulting source spectra are flat at long periods with no indication of anomalous long-period energy. Our results imply that oceanic transform earthquakes do not commonly have detectable slow rupture components.