Abstract
In this paper the question "Is there an intensity-dependent frequency shift in the Compton scattering of free electrons by high-intensity electromagnetic radiation?" is clarified. It is proven that if the electron is free, i.e., well separated from the electromagnetic beam before and after the interaction, no intensity-dependent frequency shift arises. If, on the other hand, the electron has been interacting with the electromagnetic wave train a sufficiently long time before the actual observation of a Compton scattering event, an intensity-dependent frequency shift will in fact be present.