A detailed numerical study is performed of the dynamics of optical pulse compression in an additive pulse mode-locking configuration consisting of an erbium-doped fiber laser coupled to a nonlinear optical fiber. Pulse evolution is treated by the use of an extended nonlinear Schrodinger equation incorporating a gain-and-loss term in the active fiber laser and a loss term for the nonlinear fiber, which forms the nonlinear auxilliary cavity. To treat ultrashort optical pulses with durations of less than 100 fs, we have considered third-order dispersion and self-frequency shift. On the basis of extensive numerical simulations of the all-fiber coupled-cavity configuration, a stable operating range for pulse compression is identified. It is shown that a variety of less-desirable dynamical evolutions, including pulse splitting, are obtained under other operating conditions.