We show that efficient optical pulse compression can be achieved when normally dispersive nonlinear waveguide arrays are used in conjunction with dispersive elements such as gratings or other programmable phase filters. Our computations indicate that the compression resulting from such discrete arrays can be of better quality as compared to that obtained traditionally from a single nonlinear waveguide element. The performance of the array-grating compression method is assessed in normally dispersive highly nonlinear AlGaAs array systems.