In a companion paper (1), we used computer simulations to show that a strategy of activity-dependent, on-line net synaptic potentiation during wake, followed by off-line synaptic depression during sleep, can provide a parsimonious account for several memory benefits of sleep at the systems level, including the consolidation of procedural and declarative memories, gist extraction, and integration of new with old memories. In this paper, we consider the theoretical benefits of this two-step process at the single-neuron level and employ the theoretical notion of Matching between brain and environment to measure how this process increases the ability of the neuron to capture regularities in the environment and model them internally. We show that down-selection during sleep is beneficial for increasing or restoring Matching after learning, after integrating new with old memories, and after forgetting irrelevant material. By contrast, alternative schemes, such as additional potentiation in wake, potentiation in sleep, or synaptic renormalization in wake, decrease Matching. We also argue that, by selecting appropriate loops through the brain that tie feedforward synapses with feedback ones in the same dendritic domain, different subsets of neurons can learn to specialize for different contingencies and form sequences of nested perception-action loops. By potentiating such loops when interacting with the environment in wake, and depressing them when disconnected from the environment in sleep, neurons can learn to match the long-term statistical structure of the environment while avoiding spurious modes of functioning and catastrophic interference. Finally, such a two-step process has the additional benefit of desaturating the neuron’s ability to learn and of maintaining cellular homeostasis. Thus, sleep-dependent synaptic renormalization offers a parsimonious account for both cellular and systems level effects of sleep on learning and memory.