How long did it take for your sleep to normalize?

I was never a heavy smoker but I usually had some before bed each night. I was typically getting enough hours of sleep but waking up groggy and almost hung over feeling each morning. So I decided to quit smoking completely about a month and half ago. It's been great aside from the fact I'm only getting 3-5 hours of sleep a night. I'm pretty much just as exhausted as before. I know that there's a rebound effect from REM sleep suppression.. but how long can I anticipate this lack of sleep? How long did it take for yours to normalize? I thought I'd be seeing some results 6 weeks in.