  We calculate the cross section for the lepton-proton bremsstrahlung process
$l+p\to l^\prime +p+\gamma$ in effective field theory. This process corresponds
to an undetected background signal for the proposed MUSE experiment at PSI.
MUSE is designed to measure elastic scattering of low-energy electrons and
muons off a proton target in order to extract a precise value for the proton's
r.m.s. radius. We show that the commonly used {\it peaking approximation},
which is used to evaluate the {\it radiative tail} for the elastic cross
section, is not applicable for muon proton scattering at the low-energy MUSE
kinematics. We also correct a misprint in a commonly cited review article.
