I think what many people fail to realize is that the 'groggy' feeling we experience in the morning after struggling for many hours to fall asleep is largely a state brought about by our mental frame of thought. I know there will be people here who don't agree, and that's fine, but I've tried to reason the way I feel - and I've noticed that on nights when I struggle to fall alseep, I often end up lying there in frustration, trying to find something to blame, feeling disappointed about not being able to sleep, thinking something is wrong, etc. This feeling often carries over into the morning - our society has internalized the notion that anything short of 6-8 hours will make us tired, so we often subconsciously cause ourselves to feel groggy. If you don't buy this reasoning, this is the same principle of people who think positively having happier lives, more energy, etc.
I guess what I'm recommending is to just accept a couple of nights of struggling to sleep as just the normal ebb and flow of the body. We aren't machines that have strict requirements - our bodies fail from time to time, but more often than not, we wake up in the morning, and still go on with our day.
If you can realize that - and simply just relax in bed, not feeling frustrated by the notion that you will be tired the following morning, I think you'll actually fall asleep sooner, while taking a very natural route in dealing with this issue.
I know a lot of people are going to burn my suggestion for being too philosophical, but I believe this shift for people turning to drugs for every ailment and issue represents an attempt at an unattainable perfection, and an insecurity with the normal flaws of the human body.
