An external shock model for the prompt gamma-ray luminous phase of gamma-ray bursts (GRBs) is treated both analytically and numerically. A widely cited derivation claiming that an external shock model for rapidly variable GRBs must be very inefficient employs an incorrect expression for the angular timescale. Numerical results show that variable GRBs can be formed with > 10% efficiency to transform the directed kinetic energy of the relativistic fireball to gamma-rays. Successes of the external shock model and difficulties with an internal wind/colliding shell model are summarized. An impulsive external shock model is consistent with the supranova model.