I have a sleep disorder (delayed sleep phase syndrome) that responds quite well to melatonin. What I've learned from people who have gotten their DSPS under control is that, just like Evening Glory's study reported, less is more. The thing about using melatonin for sleep is that it makes you sleepy two different times.
It makes you sleepy when it first crosses into the brain, about 20-30 minutes after taking it (10-20 if you use a sublingual preparation). This effect doesn't last long, however. Maybe a half hour before it wears off. In order for this "first wave" of sleepiness to help you fall asleep, you usually need to take a big dose. Say, 3-5 mg. Sometimes even that won't be enough, because the first wave of sleepiness is often weak.
But that's a really inefficient way to use the melatonin, and it's known to cause the "foggy brain" effect the next day and make it hard to wake up in the morning. What helps more is to take a very small dose of melatonin, like 0.1-0.3 mg about 2-3 hours before you plan to sleep. The "first wave" sleepiness effect is very mild. Maybe you feel like yawning for a few minutes, but then it's gone. About 2-3 hours later, you get very calm and relaxed and -- even at such a low dose -- you may not even be able to keep your eyes open if you try. This is the way that I use it for my DSPS, because my body clock won't normally signal that it's time to go to sleep until around 4 in the morning. If I take about 0.25 mg of melatonin around 9 pm, then I can fall into a restful sleep around 11 pm, with no brain fog the next day. I call this delayed effect the "second wave" of sleepiness. If you want to use melatonin for sleep, especially for something like jet lag or other body clock disruptions like my DSPS, then low doses several hours before bedtime is the way to go.
Do note that ordinary insomnia, where you feel very tired but are unable to sleep, does not typically respond at all to melatonin. This is because only the weak first wave effect of melatonin directly causes sleepiness. The stronger second wave does not directly tell your brain to sleep. It tells your brain that it's night time, which (in the absence of insomnia) makes you feel sleepy. For jet lag, DSPS, or trying to go to bed earlier than usual, this is great. But when you have insomnia, the body clock is already saying that it's night time. That's why you feel so tired. Melatonin won't help in this case because it's the solution to a problem that insomniacs don't have (the problem being a body clock that doesn't think that it's night time). So if you are exhausted but you just can't seem to sleep, melatonin is probably not going to be helpful.
It might be interesting to test the effects of melatonin on spice if the spice is used between the first and second waves, because there's about an hour and a half where you don't feel sleepy even though the melatonin is in your system.