C.M.
M., I had the same exact problem with my son. And no matter how I centered him in his bassinett, he would roll onto his tummy, scoot himself over and would end up smashing his face against the side-rails.
I got a sleep positioner and it solved the problem. Here's the link to the product:
http://www.toysrus.com/product/index.jsp?productId=258566...
Good luck and hope you get some sleep!!!!!!!!!!!!!!!!!
C.