Wake up at three am, The Caterpillar's normal feeding time. Watch her kick and fuss for about an hour or so and then fall back to sleep. Swaddle her and put her in the bassinet next to your bed, then climb back into bed to try and grab a couple more hours' sleep before you have to get up and deal with the day. Lie there awake for two minutes. Spend an hour having the following conversation with yourself:
The baby is not making much noise, I wonder if she's not breathing.

Of course she's breathing. She's not making noise because she's sleeping.

I should check.

You should be sleeping too. She is asleep. You do not need to check.

But she's really quiet.

You will not obsessively check to see if that baby is breathing every ten minutes throughout the night!!

If she suffocates while sleeping in her bassinet right next to my bed while I'm casually sleeping away right next to her, I would feel like a pretty poor mother.

You do not need to check and see if that baby is breathing... you put her down less than three minutes ago.

But that blanket she's wrapped in is pretty soft... make she wiggled out of it and is suffocating in its folds.

She has not made any sounds that would indicate she is in any distress.

Yes, but if she had stopped breathing, I wouldn't be hearing anything, would I?

If you don't sleep now while you have the chance, you will not get a chance. The baby is fine.

If I don't check on her now, I won't be able to sleep at all.
Give in.

Get up from bed and put hand on baby's chest to confirm that she is breathing.

She is.

Go back to bed, now satisfied that she is alive and confident you can sleep.

Lay back down.

Baby wakes up five minutes later.

My internal monologue is a little bit nuts.