For very high data rate optical communication systems, jitter is an impairment which may seriously degrade system performance. Previously reported methods for performance assessment of optical communication systems in the presence of jitter require the jitter probability distribution to be known. More commonly, only limited information is available, such as the measured jitter variance and the peak to peak range of the jitter. Assuming knowledge of the jitter statistics to be restricted to just the range and RMS value, we determine in this paper a new upper bound on the performance. For a certain class of signals, we derive a worst-case distribution (WCD) which consists of three Dirac impulses, located at the centre and at the extremes of the range. The usefulness of the WCD is demonstrated by means of examples which show that for many practical cases the new bound is tight. We show how the WCD may be combined with a modified Chernoff bound to obtain an overall upper bound on system performance which encompasses a comprehensive set of impairments including jitter. Since this requires only the range and RMS value of the jitter to be known, it provides a distribution free technique for assessing the influence of jitter on the performance of optical communication systems.