At high luminosities black hole binaries show spectra with a strong disc component accompanied by an equally strong tail where at least some of the electrons are non-thermal. We reanalyze the simultaneous ASCA-RXTE-OSSE data from the 1998 outburst of XTE J1550-564, which span 0.7-1000 keV and remain the best data available of a black hole binary in this state. We reassess the importance of electron-positron pair production using a realistically high value of the source compactness for the first time. The lack of an observable annihilation line together with the observed gamma-ray flux beyond 511 keV constrains the maximum electron Lorentz factor to be leq 10 and the slope of the injected electrons to leq 2.5. We also use the fast (10-50 Hz) variability spectrum to constrain the spatial dependence of the electron heating and acceleration. We find that the spectrum of the fast variability is consistent with being fully thermal, so that the observed non-thermal emission is produced from further out in the flow.
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