You might want to try f.lux. Since the problem with electronic devices seems to be blue light, changing the hue of the screen to a more reddish tone seems to prevent the serotonin production inhibition associated with blue light.
I love f.lux. I don't know if it has actually helped me fall asleep faster, but I find myself getting a lot less eye strain when working at night. I just wish I could find a similar app that actually works well for android. Any suggestions out there?
For many of us this will be the hardest part (and also a large source of sleep problems).