Sleep is conserved from invertebrates to vertebrates, and is tightly regulated in a homeostatic manner. The molecular and cellular mechanisms that determine the amount of rapid eye movement sleep (REMS) and non-REMS (NREMS) remain unknown. Here we identify two dominant mutations that affect sleep and wakefulness by using an electroencephalogram/electromyogram-based screen of randomly mutagenized mice. A splicing mutation in the Sik3 protein kinase gene causes a profound decrease in total wake time, owing to an increase in inherent sleep need. Sleep deprivation affects phosphorylation of regulatory sites on the kinase, suggesting a role for SIK3 in the homeostatic regulation of sleep amount. Sik3 orthologues also regulate sleep in fruitflies and roundworms. A missense, gain-of-function mutation in the sodium leak channel NALCN reduces the total amount and episode duration of REMS, apparently by increasing the excitability of REMS-inhibiting neurons. Our results substantiate the use of a forward-genetics approach for studying sleep behaviours in mice, and demonstrate the role of SIK3 and NALCN in regulating the amount of NREMS and REMS, respectively.