Abstract—We propose chip waveforms for essentially fullresponse signaling in DS-CDMA systems that employ offset quadrature modulation formats. The waveforms are optimal in the sense that for a given out of band power leakage, the transmit signal occupies the minimum inband power bandwidth. At the same time, certain smoothness conditions on the phase and envelope of the transmit signal in the time domain are satisfied. The performance of the respective modulation schemes is compared with that of conventional techniques including MSK and time-domain raised-cosine pulses. Numerical results indicate a significant gain in system capacity compared to conventional pulses, and near optimality with respect to interference rejection.