Slow-wave sleep is thought to be important for retuning cortical synapses, but the cellular mechanisms remain unresolved. During slow-wave activity, cortical neurons display synchronized transitions between depolarized Up states and hyperpolarized Down states. Here, using recordings from LIII pyramidal neurons from acute slices of mouse medial entorhinal cortex, we find that subthreshold inputs arriving during the Up state undergo synaptic weakening. This does not reflect a process of global synaptic downscaling, as it is dependent on presynaptic spiking, with network state encoded in the synaptically evoked spine Ca2+ responses. Our data indicate that the induction of synaptic weakening is under postsynaptic control, as it can be prevented by correlated postsynaptic spiking activity, and depends on postsynaptic NMDA receptors and GSK3β activity. This provides a mechanism by which slow-wave activity might bias synapses towards weakening, while preserving the synaptic connections within active neuronal assemblies.Slow oscillations between cortical Up and Down states are a defining feature of deep sleep, but their function is not well understood. Here the authors study Up/Down states in acute slices of entorhinal cortex, and find that Up states promote the weakening of subthreshold synaptic inputs, while suprathreshold inputs are preserved or strengthened.