The spike generating mechanism of cortical neurons is highly reliable, able to produce spikes with a precision of a few milliseconds or less. The excitatory synapses driving these neurons are by contrast much less reliable, subject both to release failures and quantal fluctuations. This suggests that synapses represent the primary bottleneck limiting the faithful transmission of information through cortical circuitry. How does the capacity of a neuron to convey information depend on the properties of its synaptic drive? We address this question rigorously in an information theoretic framework. We consider a model in which a population of independent unreliable synapses provides the drive to an integrate-and-fire neuron. Within this model, the mutual information between the synaptic drive and the resulting output spike train can be computed exactly from distributions that depend only on a single variable, the interspike interval. The reduction of the calculation to dependence on only a single variable greatly reduces the amount of data required to obtain reliable information estimates. We consider two factors that govern the rate of information transfer: the synaptic reliability and the number of synapses connecting each presynaptic axon to its postsynaptic target (i.e., the connection redundancy, which constitutes a special form of input synchrony). The information rate is a smooth function of both mechanisms; no sharp transition is observed from an "unreliable" to a "reliable" mode. Increased connection redundancy can compensate for synaptic unreliability, but only under the assumption that the fine temporal structure of individual spikes carries information. If only the number of spikes in some relatively long-time window carries information (a "mean rate" code), an increase in the fidelity of synaptic transmission results in a seemingly paradoxical decrease in the information available in the spike train. This suggests that the fine temporal structure of spike trains can be used to maintain reliable transmission with unreliable synapses.