Is it ok for baby to sleep on his tummy once he can pick his head up?

I know all about "back to sleep" and risk of SIDS but I am not sure if it's ok to put them on their tummy when they can lift their head and turn it side to side. My first son slept on his back. No problem. This time around baby boy number 2 won't sleep unless he's on his tummy so I STILL end up with sleepless nights because of course I stay up to make sure he's sleeping safely. Help!!