Is sleeping in the Rock N Play safe?

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My baby is a week old today and for the first 4 nights home I had her sleep in the co sleeper bed I bought. It goes directly next to my bed and is the recommended firm flat mattress for babies to sleep on. She slept awful in it. On the fifth night me and my fiancé were exhausted and put her in her rock n play. She slept wonderfully. So we did it again the next night and she slept great again. But I’m extremely paranoid about SIDS! Is the rock n play safe enough or should I just deal with her crying all night and move her back to the co sleeper bed? I just want what’s best for my baby!

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