We assess non-thermal Comptonization models for the high-energy emission of the EGRET blazar sources. We argue that the copious γ-ray radiation originates from a region that is transparent to pair-production processes, at some distance from the central engine. In the opposite case, the absorbed γ power would be largely reprocessed into softer X-ray photons, contrary to the observations. Our model consists of a low-entropy inner jet and a dissipative outer jet, where the kinetic or Poynting primary flux is converted into energetic emitting particles. We show that most of the dissipation is likely to occur as the outflowing material approaches the broad-line region (BLR). The radiation produced by BLR clouds illuminated by the relativistically moving plasma ‘blob’ provides the bulk of the seed photons to be Comptonized to γ energies. The strong interplay between the cooling blob and BLR material results in a flare of γ photons when the blob crosses the BLR shell. Our model predicts this flare to lag the optical outburst. It also predicts almost simultaneous variability at all γ energies.