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

Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares