Facilitation is a transient stimulation-induced increase in synaptic response, a ubiquitous form of short-term synaptic plasticity that can regulate synaptic transmission on fast time scales. In their pioneering work, Katz and Miledi (1968) and Rahamimoff (1968) demonstrated the dependence of facilitation on presynaptic Ca²⁺ influx, and proposed that facilitation results from the accumulation of residual Ca²⁺ bound to vesicle release triggers. However, this bound Ca²⁺ hypothesis appears to contradict the evidence that facilitation is reduced by exogenous Ca²⁺ buffers. This conclusion led to a widely-held view that facilitation must depend solely on the accumulation of Ca²⁺ in free form. Here we consider a more realistic implementation of the bound Ca²⁺ mechanism, taking into account spatial diffusion of Ca²⁺, and show that a model with slow Ca²⁺ unbinding steps can retain sensitivity to free residual Ca²⁺. We demonstrate that this model agrees with the facilitation accumulation time course and its biphasic decay exhibited by the crayfish inhibitor neuromuscular junction (NMJ), and relies on fewer assumptions than the most recent variants of the free residual Ca²⁺ hypothesis. Further, we show that the bound Ca²⁺ accumulation is consistent with the experimental results of Kamiya and Zucker (1994), which revealed that photolytic liberation of a fast Ca²⁺ buffer decreases the synaptic response within milliseconds. We conclude that Ca²⁺ binding processes with slow unbinding times (tens to hundreds of milliseconds) constitute a viable mechanism of synaptic facilitation at some synapses, and discuss the experimental evidence for such a mechanism.