Pulse shaping is examined as a means to improve the performance of a differential offset quadrature phase-shift keying system in a bandwidth-constrained environment. Through optimization with respect to a composite Nyquist criterion, the derived pulse shapes have comparable performance to a /spl pi//4-differential quadrature phase-shift keying in an additive white Gaussian noise (AWGN) channel and better performance in a hard-limited AWGN channel.