A stochastic model of spike-timing-dependent plasticity proposes that single synapses express fixed-amplitude jumps in strength, the amplitudes being independent of the spike time difference. However, the probability that a jump in strength occurs does depend on spike timing. Although the model has a number of desirable features, the stochasticity of response of a synapse introduces potentially large fluctuations into changes in synaptic strength. These can destabilize the segregated patterns of afferent connectivity characteristic of neuronal development. Previously we have taken these jumps to be small relative to overall synaptic strengths to control fluctuations, but doing so increases developmental timescales unacceptably. Here, we explore three alternative ways of taming fluctuations. First, a calculation of the variance for the change in synaptic strength shows that the mean change eventually dominates fluctuations, but on timescales that are too long. Second, it is possible that fluctuations in strength may cancel between synapses, but we show that correlations between synapses emasculate the law of large numbers. Finally, by separating plasticity induction and expression, we introduce a temporal window during which induction signals are low-pass-filtered before expression. In this way, fluctuations in strength are tamed, stabilizing segregated states of afferent connectivity.