I experienced something similar on the ketogenic diet. When I was on 0 carbs, I would wake up at 5am (sometimes 4am), wide awake and feeling rested, looking forward to breakfast! Some nights I'd wake up, feeling wide awake, in the middle of the night (2-3am), after which I'd go for a smoke and then back to sleep again for a couple of hours (smoking actually helped me feel wanting to go back to sleep). I don't think I ever slept and felt rested after only 3 hours, though, but people are different. I personally think it's natural, and perhaps you will revert back to 6-7 hours at some point? I'd say keep a close eye on how things go.
I also have experienced a similar effect of the lower carb ketogenic/paleo now leaning more towards the Carnivore diet. I was attributing the need for less sleep mostly to the smoking aspect but after reading some other's experience I see it can also be the effects of the diet.
I still think smoking has been a part of my requiring less sleep too. I know this thread is more about the Carnivore diet but the sleep observations may relate to the benefits of smoking. But smoking is not for everyone.
Session 27 June 1998:
Q: What altered my chosen balancing mechanism?
A: First: what is your chosen balancing mechanism?
Q: Do you mean something physical in my body?
A: Close.
Q: I don't know. Going to the gym?
A: No.
Q: Something about the way I work or function?
A: No. Something you, or one, takes into the body.
Q: Thyroid pills?
A: This substance raises hemoglobin levels.
Q: What?! I quit smoking?!
A: Yes.
Q: How can smoking be a balancing mechanism?
A: Speeds up metabolism, thus allowing greater food intake.
Q: Well, all it did for me was allow me to eat at all! I guess that now I will have to quit eating completely forever!
A: Or bring nicotine back.
Q: Well, that's not gonna happen! Isn't there something else that would work?
A: No.
Q: So, you are saying that nicotine is actually good for me?
A: Yes. Without it, you will remain with weight problems, because you will not be able to lower food intake enough to compensate. Why do you think you had the inkling to start smoking in the first place?
Q: Well, I just was going along with my friends, I thought.
A: No.
Q: What other things does nicotine do?
A: Raises defences.
Q: What kind?
A: Immunological.
Q: Anything else?
A: Excites neurotransmitters. You require less sleep.
Q: Is this true for everyone?
A: No.
Q: (A) How much nicotine is necessary?
A: 100 mg per day.
Q: (A) Can it be in pill form?
A: Cigarettes infuse it to brain tissues most effectively.