We demonstrate almost chirp-free and pedestal-free optical pulse compression in a nonlinear fiber Bragg grating with exponentially decreasing dispersion. The exponential dispersion profile can be well approximated by a few gratings with different constant dispersions. The required number of sections is proportional to the compression ratio, but inversely proportional to the initial chirp value. We propose a compact pulse compression scheme, which consists of a linear grating and a nonlinear grating, to effectively compress both hyperbolic secant and Gaussian shaped pulses. Nearly transform-limited pulses with negligibly small pedestal can be achieved.