Bandlimited offset QPSK systems are analysed and attempts are made to find new combinations of transmit and receive filters which give improved performance trade-offs when compared with recently proposed filters such as quadrature overlapped raised-cosine (QORC) and squared raised-cosine (QOSRC), and superposed quadrature amplitude modulation (SQAM). The filters are based on finite impulse responses of up to five symbol periods (ten bit periods) duration. The results indicate that advantages can be gained over QORC, QOSRC and SQAM, if a good performance with linear channels is required as well as low degradation under hard limiting. This probably also implies good performance under soft limiting. The results are presented graphically, showing how the bit error rate performance with each filter pair degrades as the adjacent channel spacing of the system is reduced.