Weakly coherent optical communication systems, in which the receiver measures the signal power within a passband determined by the IF filter without using phase information in the signal, can be designed to accommodate severe laser phase noise. This paper compares theoretical predictions for the effect of phase noise on these systems, using the models of Garrett and Jacobsen, Kazovsky, and of Foschini and co-workers, and models derived from them. For total line-widths of less than about the bit rate, all these models agree reasonably well in predicting the IF bandwidth required to accommodate the phase noise. For larger linewidths, it is shown that significantly narrower IF filters may be used than has been predicted by any model published previously. As examples, it is predicted that effective IF bandwidths of about six and eleven times the data rate can accommodate total linewidths of as much as three and ten times the data rate, respectively.