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It is best to get proper rest if at all possible. I have found short cat naps helpful... if there is time. Then I can wake refreshed and stay awake during meditation. It is better to have a short meditation awake then a long one nodding off regularly. For me I have found there is no better condition then proper sleep. This has been a hard lesson I have learned for years of trying to meditate exhausted. All it did was led to bad meditation practices of being in no man's land between sleep and wakefulness: a passive state and blankness of the mind.
Yes, I learned that pretty soon, my first year of meditation practice, very eager, I used to get up and meditate at 4 am, but really what I was doing was sleeping in a cross-legged postures, sleeps or hallucinations since I found I could mantain the sitting posture. Sheer will power is not always the winning strategy.