Variation in the amplitude of miniature postsynaptic currents (mPSCs) generated by individual quanta of neurotransmitter is a major contributor to the variance of evoked synaptic responses. Here we explore the possible origins of this variability by developing a mathematical description of mPSC generation and consider the contribution of "off-center" release to this variability. By "off-center" release we mean variation in the distance between the position where a presynaptic vesicle discharges its content of neurotransmitter into the synaptic cleft and the center of a cluster of postsynaptic receptors (PRCs) that responds to those transmitter molecules by generating an mPSC. We show that when the time course of quantal discharge through a fusion pore (noninstantaneous release) is considered, elementary analytical descriptions of the subsequent diffusion of transmitter within the synaptic cleft (with or without uptake) predict the development of significant gradients of transmitter concentration during the rising phase of mPSCs. This description of diffusion is combined with a description of the pharmacodynamics of receptors in the PRC and of the time dependence of the gradient of transmitter concentration over the area of the PRC to reconstruct the time course and amplitude of an mPSC for a synapse of a given geometry. Within the constraints of known dimensions of presynaptic active zones and postsynaptic receptor clusters at CNS synapses, our analysis suggests that "off-center" release, produced by allowing release to occur anywhere within an anatomically defined presynaptic active zone, can be an important contributor to mPSC variability. Indeed, modulation of the influence of "off-center" release may be a novel way of controlling synaptic efficacy. We also show how noninstantaneous release can serve to focus the action of neurotransmitter within a given synapse and thereby reduce cross-talk between synapses.