Babies do tend to sleep better on their bellies, but it's better for them to sleep on their backs, to avoid SIDS.  However, once my daughter learned to roll herself over, she has slept on her tummy, and our pediatrician said that was ok.  She was older than 4 months, though.  We never swaddled her, and she learned to go back to sleep after flailing herself awake.  I would talk to your pediatrician about belly vs back.

My DD has slept on her belly since she was 1 month old.  I know people panic about SIDS, but I did just like you.  I put her down on her belly during naps.  I kept a very close eye on her.  Since she was able to pick her head up without any problems and she slept great during naps on her belly, I figured what is the difference at night.  She is 8 months old now and still sleeps on her belly. 

All doctors will recommend that you baby sleep on his back at night, because of SIDS.  Also keep in mind that a baby may not know that he is lacking oxygen  if something obstucts his breathing during the night.  I always made sure that my boys could not turn over onto their tummy at night.  I thought it best to be safe than sorry.

 If a baby rolls himself over, I believe I've read that it's okay for them to sleep on their tummy (meaning, if they roll over to their tummy, themselves, in the night).

 I guess you have to weigh the risk factors:  If the baby is drinking formula, or if a parent is a smoker, then the risks are higher for SIDS than if the baby is breastfed in a non-smoking family.  But, the AAP definitely encourages moms to put their babies on their backs.

 One idea I have:  Wait until she's asleep, and then roll up two receiving blankets the long way and tuck one under each side of her (behind the shoulders so she won't have her airflow compromised).  That is what helped my babies from startling so much at night.

 Hugs!

My baby girl died 11yrs ago... in her sleep.. from SIDS.. on her tummy.... She was 5mos old , and had learned to roll in her sleep on her own....

Believe me! I NEVER in a million years thought it would happen to us.  I turned out ok, and I slept on my tummy right ??? 

Well, since that morning I've never been able to stand seeing a baby sleep on their tummy..  So take it from me...  Its simply NOT WORTH IT !

 the statistics on tummy sleeping are clear.  and yes, there comes a point that you cant keep them on their backs... but until that point, do your best to keep baby on his/her back.  Its worth the effort and loss of any sleep...