I used to do a very low carb diet that kept me in ketosis. For the most part it was great but the sleep difference concerned me. At the time my life was structured to where I didn't need to be awake at any particular time so my body would wake up when it had enough sleep instead of when an alarm went off. While I usually sleep seven to eight hours when eating a standard American diet, when on low carb, it would end up being only five to six hours, usually closer to five than six. I'd feel completely rested and fine but most days I'd need to take a short ten to fifteen minute nap, during which I'd quickly fall into REM sleep. When waking up from that nap, I'd feel fine, no post-nap grogginess, but it made me wonder if I was getting shorted on REM sleep during my primary sleep period.