An unresolved paradox exists in auditory and electrosensory neural systems {Carr93,Heiligenberg91}: they encode behaviourally relevant signals in the range of a few microseconds with neurons that are at least one order of magnitude slower. We take the barn owl's auditory system as an example and present a modeling study based on computer simulations of a neuron in the laminar nucleus. Three observations resolve the paradox. First, spiking of an integrate-and-fire neuron driven by excitatory postsynaptic potentials (EPSPs) with a width at half maximum of 250 microseconds has an accuracy of 25 microseconds if the presynaptic signals arrive coherently. Second, the necessary degree of coherence in the signal arrival times can be attained during ontogenetic development by virtue of an unsupervised Hebbian learning rule. Learning selects connections with matching delays from a broad distribution of axons with random delays. Third, the learning rule also selects the correct delays from two independent groups of inputs, for example, from the left and right ear.