In terms of 'zeitgeibers', you can strengthen the circadian day/night cues which can help with how quickly sleep arrives (and stimulate release of melatonin in the brain). Remove every daylight-white lightbulb in the house and replace them with dimmer, warm-white ones. Avoid CFLs and opt for LEDs if you can. Adjust the telly or any other screens that are on in the evening to minimum levels of blue, and reduce the brightness. Reduce the overall lighting a couple of hours before bed. Same goes for temperature, especially in the sleeping space. Then make sure you get out into daylight in the morning each day.

My DD really isn't happy in a completely dark room, so we got a cheap red lamp from Ikea and fitted it with the dimmest light bulb we could find. Red light is the least stimulating (in terms of suppressing melatonin and stimulating wakefulness) so this was a good solution for us, and it certainly helped with DD's anxiousness. We have also done distraction in the form of soothing music and short kids audiobooks on the stereo. It's not a complete solution but every little bit helps.