Although synchrotron radiation is thought to be well understood in a theoretical sense, the practicalities of controlling a synchrotron source sometimes seem difficult. Often the output spectrum contains sharp peaks, especially at the high-frequency end of the spectrum. These spikes are unwanted because they rob power from desired frequency intervals, and unexpected because idealized theory predicts a quite smooth spectrum. In the face of such difficulties, it has been natural to suspect some sort of engineering shortfall. But the present paper argues that the spectral structure may point instead to an imperfection of theory.