Approximate formulae for the instantaneous scattered radiation spectra are derived in the Thomson and Klein-Nishina regimes, assuming that the relativistic electrons are described by an isotropic angular and power-law energy distribution in the outflowing fluid frame. The soft photon source is assumed to be axially symmetric. We find that the Thomson-limit luminosity enhancement in the direction that the scattered radiation is most intense varies as Γ6 for photons entering from the side and as Γ2 for photons entering directly from behind, where Γ is the bulk Lorentz factor of the outflowing plasma cloud. Energy loss and flow are treated in a model where energetic electrons are instantaneously injected with a power-law energy distribution at some height above a point or disk photon source, and instantaneous and time-average spectra are calculated. We also treat the electron energy-loss rate and scattered photon spectra from photon fields that are isotropic in the stationary frame.We calculate broad-band spectra for the case where soft photons are produced by a cool blackbody outer disk extending to the innermost stable orbit of a Schwarzschild black hole, and fit these results to observations of high-energy radiation from 3C 279, 3C 273, and Mrk 421. The observed spectral softening in the regime between hard X-ray and >100 MeV gamma-ray energies is attributed to the transition from an uncooled to a cooling electron distribution, yielding a break of 0.5 units in the scattered photon spectra index.