Fine temporal patterns of firing in much of the brain are highly irregular. In some circuits, the precise pattern of irregularity contains information beyond that contained in mean firing rates. However, the capacity of neural circuits to use this additional information for computational purposes is not well understood. Here we employ computational methods to show that an ensemble of neurons firing at a constant mean rate can induce arbitrarily chosen temporal current patterns in postsynaptic cells. If the presynaptic neurons fire with nearly uniform interspike intervals, then current patterns are sensitive to variations in spike timing. But irregular, Poisson-like firing can drive current patterns robustly, even if spike timing varies by tens of milliseconds from trial to trial. Notably, irregular firing patterns can drive useful patterns of current even if they are so variable that several hundred repeated experimental trials would be needed to distinguish them from random firing. Together, these results describe an unrestrictive set of conditions in which postsynaptic cells might exploit virtually any information contained in spike timing. We speculate as to how this capability may underlie an extension of population coding to the temporal domain.