A study is made of the relationship between pulse shaping and intersymbol interference, in a pulse communication system, where the message is represented by a pulse train of infinite length with random pulse polarity. Pour received pulse signal shapes are derived by sending rectangular and raised cosine pulses through first and second order channels with d.c. gains of unity. Additive white noise is assumed throughout the study. A comparison is made of three receivers using signal-noise (power) ratio (SNR) as the performance criterion. The receivers are the ordinary matched filter followed by a sampler, the ideal (i.e. optimum) receiver which includes a sampled-data intersymbol interference compensator, and an approximation to the ideal receiver, in which the ^compensator is a digital tapped delay line with 3 taps. Five cases are covered: minimization of channel bandwidth, under constraints of constant average transmitter power, and constant pulse amplitude (peak power); maximization of pulse repetition rate, under the same two constraints; and constant received signal power. The study shows that the raised cosine pulse gives slightly better SNR and requires less channel bandwidth than the rectangular, under the constant average power constraint, while the rectangular pulse is better under the constant pulse amplitude constraint. Pulse repetition rate may be increased up to two times by use of the 3-tap receiver and appropriate signal shape. The benefits to be realized from guard spaces between transmitted pulses, or overlapping of transmitted pulses, are amply demonstrated. In many instances, the performance of the 3-tap receiver closely approaches that of the ideal, indicating that it may be a useful practical approximation to the ideal receiver.