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We investigated how the two properties short-term synaptic depression of afferent input and postsynaptic firing dynamics combine to determine the operating mode of a neuron. While several computational roles have been ascribed to either, their interaction has not been studied. We considered two types of short-term synaptic dynamics (release-dependent and release-independent depression) and two classes of firing dynamics (regular firing and firing with spike-frequency adaptation). The input-output transformation of the four possible combinations of pre- and postsynaptic dynamics was characterized. Adapting neurons receiving input from release-dependent synapses functioned largely as coincidence detectors. The other three configurations showed properties consistent with integrators, each with distinct features. These results suggest that the operating mode of a neuron is determined by both the pre- and postsynaptic dynamics and that studying them together is necessary to understand emergent properties and their implications for neuronal coding.