Some simple things that make a big difference here--
-White noise- lots of it
-A dark room, I know you say you don't turn on any lights, but some peoples rooms are just light anyway. For my little ones the darker the better.
-Comfortable temp, and pjs. This can very so much, you have to find out what works for your kid. My middle has always slept much better cold then in pjs. From the time he was a newborn, he slept better in just a diaper. For many kids tags or organic pj can sometimes help.
-Comfortable humidity. Espcially in the winter, a dry stuffy nose can make it more difficult to sleep soundly.
None of these are magic cures, just things that seem to make my kids more likely to roll over and go back to sleep after a mild disturbance then wake all the way up.