I've been doing it wrong:

But, I can’t sleep When you can’t sleep, should you lie in bed with your eyes closed? No. Brian Fung answers in the Atlantic.

The useful takeaway is that your best move, if you’ve been in bed for 20 minutes and still aren’t dozing off, is to get up and engage in a low-light, low-stress activity like reading until you begin to feel tired. Taking your mind off of “Why am I not sleeping?! I need to sleep!” is crucial. When you do get up, though, don’t use your computer or phone or watch TV — the blue-colored light from the screens tricks your body into thinking it’s daytime and not releasing melatonin.

That's a good tip: read, but not with a screen. I wonder if a Kindle is okay?