We report the results of an accurate analysis of the effect of filtering on phase noise, appropriate to coherent optical receivers with delay demodulation. Based on a numerical solution of a Fokker–Planck equation, we show that the phase at the output of the IF filter is very closely a Gaussian random process. The variance of phase fluctuations over a time equal to the integration time of the filter is reduced by a factor of 0.363. We show that receivers with minimum IF bandwidth can therefore operate with about 1.36 times the laser linewidth predicted disregarding the filtering effect We outline a route to analysing the performance of receivers with broader than optimum IF filters.