A precise measurement of the spectrum of the photons from ep bremsstra
hlung with the ZEUS luminosity monitor at HERA is reported. The measur
ement shows a reduced rate compared to the Bethe-Heitler spectrum for
photon energies below 5 GeV. This suppression, called the beam-size ef
fect, is explained by the finite transverse size of the beam overlap r
elative to the typical impact parameter in the process of ep bremsstra
hlung at HERA energies.