Recent evidence suggests that low and high firing neurons display different plasticity and dynamics. Here, we rank-ordered rat hippocampal CA1 units by firing rate and implemented a shuffle-correction to account for regression-to-the-mean. We found that sleep/wake states and state transitions affected lower and higher-firing neurons differently. Firing-rate changes within non-REM sleep, REM sleep, and state transitions from non-REM to REM all favored higher-firing neurons, with either smaller increases or stronger decreases among lower-firing neurons. In contrast, transitions from REM to non-REM sleep resulted in higher firing among lower-firing neurons and vice versa. In sum, these patterns yielded a net decrease of firing rates across sleep, with the largest decrease occurring in lower-firing cells, and a net increase over waking, with median quantiles showing the largest firing increases. Our results suggest greater plasticity in lower firing neurons and show that non-REM sleep plays a uniquely normalizing role in sleep.