The release of neurotransmitters from synapses obeys complex and stochastic dynamics. Depending on the recent history of synaptic activation, many synapses depress the probability of releasing more neurotransmitter, which is known as synaptic depression. Our understanding of how synaptic depression affects the information efficacy, however, is limited. Here we propose a mathematically tractable model of both synchronous spike-evoked release and asynchronous release that permits us to quantify the information conveyed by a synapse. The model transits between discrete states of a communication channel, with the present state depending on many past time steps, emulating the gradual depression and exponential recovery of the synapse. Asynchronous and spontaneous releases play a critical role in shaping the information efficacy of the synapse. We prove that depression can enhance both the information rate and the information rate per unit energy expended, provided that synchronous spike-evoked release depresses less (or recovers faster) than asynchronous release. Furthermore, we explore the theoretical implications of short-term synaptic depression adapting on longer time scales, as part of the phenomenon of metaplasticity. In particular, we show that a synapse can adjust its energy expenditure by changing the dynamics of short-term synaptic depression without affecting the net information conveyed by each successful release. Moreover, the optimal input spike rate is independent of the amplitude or time constant of synaptic depression. We analyze the information efficacy of three types of synapses for which the short-term dynamics of both synchronous and asynchronous release have been experimentally measured. In hippocampal autaptic synapses, the persistence of asynchronous release during depression cannot compensate for the reduction of synchronous release, so that the rate of information transmission declines with synaptic depression. In the calyx of Held, the information rate per release remains constant despite large variations in the measured asynchronous release rate. Lastly, we show that dopamine, by controlling asynchronous release in corticostriatal synapses, increases the synaptic information efficacy in nucleus accumbens.