  Although both electron-ion and electron-electron bremsstrahlung contribute to
the hard X-ray emission from solar flares, the latter is normally ignored. Such
an omission is not justified at electron (and photon) energies above $\sim 300$
keV, and inclusion of the additional electron-electron bremsstrahlung in
general makes the electron spectrum required to produce a given hard X-ray
spectrum steeper at high energies.
  Unlike electron-ion bremsstrahlung, electron-electron bremsstrahlung cannot
produce photons of all energies up to the maximum electron energy involved. The
maximum possible photon energy depends on the angle between the direction of
the emitting electron and the emitted photon, and this suggests a diagnostic
for an upper cutoff energy and/or for the degree of beaming of the accelerated
electrons.
  We analyze the large event of January 17, 2005 observed by RHESSI and show
that the upward break around 400 keV in the observed hard X-ray spectrum is
naturally accounted for by the inclusion of electron-electron bremsstrahlung.
Indeed, the mean source electron spectrum recovered through a regularized
inversion of the hard X-ray spectrum, using a cross-section that includes both
electron-ion and electron-electron terms, has a relatively constant spectral
index $\delta$ over the range from electron kinetic energy $E = 200$ keV to $E
= 1$ MeV. However, the level of detail discernible in the recovered electron
spectrum is not sufficient to determine whether or not any upper cutoff energy
exists.
