One of the best ways to get more REM sleep is to simply add anywhere from 10 minutes to 30 minutes to your sleep schedule, adding that 10 to 30 minutes in the morning. Most people can't do that, however. Another way to increase the amount of rapid eye movement sleep that you get is to get a bigger surge of epinephrine or adrenaline in the early day prior to that sleep. So this is a great reason to do deliberate cold exposure in your shower in the morning. You could also get it through exercise.