Ever since I learned about my sleep cycle, I've made a concerted effort to wake up at the end of my REM sleep cycle. Often this means opting to get 4.5 hours of sleep instead of 5.5 hours, since my sleep cycle is 90 minutes. If I wake up mid-cycle, I'm groggy for the rest of the day.
Recently, I've been experimenting with ways to make sure that I wake up at the right time. Instead of staying up an extra hour when I'm tired, I've started setting two alarms. One 1.5 hours before I intend to wake up and one when I actually want to get out of bed. This way when the first alarm goes off, I wake up briefly but can quickly go back to bed and get one more sleep cycle before I start my day.