Alcohol's reputation as a sleep aid is only half right. Research on sleep architecture — the pattern of stages your brain cycles through overnight — shows a clear dose-response relationship: even a low dose (roughly two standard drinks) delays the onset of REM sleep and shortens how long you spend in it, and the disruption gets worse as the dose increases.
At higher doses (around five standard drinks), the picture gets more complicated. Some studies find alcohol shortens the time it takes to reach deep sleep and increases the amount of deep sleep early in the night. But that early "boost" comes at a cost later on: as your body metabolizes the alcohol, sleep becomes more fragmented, with more wakefulness in the second half of the night.
Interestingly, research following people over consecutive nights of drinking suggests the body adapts somewhat — the disruption is most pronounced on the first night and becomes less severe over the following nights. That's a tolerance effect, though, not a green light: REM disruption in particular tends to persist even as other effects fade. If you do drink, more of a gap between your last drink and bedtime gives your body more time to clear it before sleep architecture is affected.
Further reading: The effect of alcohol on subsequent sleep (ScienceDirect), Altered sleep architecture following consecutive nights of pre-sleep alcohol (SLEEP journal).