jeta1,
Consider yourself in the same boat as me old mate!!I regurlarly suffer from sleepless nights, well not exactly sleepless nights but I do have serious trouble getting off to sleep.I think you are spot on with the bit about "switching off", that is my biggest problem really!
03:00 hrs is my normal "nodding off" time and this is a pain if I'm on earlys the next day.
I had an idea that maybe my sleeping patterns are "out of shape" so-to-speak.E.g:03:00 I fall asleep, 11:30 I wake up.This is not good for when that early morning comes around!But what can you do when you simply cannot nod off?Have an early night?
My advice to you would be

n those nights when you are feeling tired at 20:00-go to bed THEN.Ok ,you may not drop off immediately but after a few early nights I think your body would soon get into the routine.This has worked for me in the past.
Another idea which I find makes you ready for sleep is going for a jog!Seriously, this tires you out and hey-presto!This is doing the biz for me at the moment anyway.
Hope that helps.As for me, well I work till midnight most nights so my sleeping habbits are unorthodox to say the least!
All the best though.
Oh check out the time I posted this message....says it all!
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And up we go!