Activity-dependent synaptic depression is a striking feature of synaptic transmission between neocortical pyramidal neurons. It has been shown that this kind of synaptic dynamics permits the transmission of rate changes rather than the DC part of presynaptic activities. In this paper, we show that activity-dependent depression makes synapses sensitive to reductions of presynaptic activity which are brief compared to the recovery time scale of the synapse. This surprising finding suggests that the synchronous lack of activity is potentially relevant for neuronal information processing. We present a mathematical analysis and an intuitive explanation of this paradoxical phenomenon.