How do you get 4wk old back to sleep in the night?

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Our FF DD is four weeks old and has a reasonable evening routine (she sleeps for three or so hours in the evening and from midnight until 3:30am ish).

But after her 3:30am waking (when she is fed, changed if necessary and cuddled, all in a quiet, dark room) she finds it really hard to go back to sleep and is all beady-eyes and whinges until 7am (when she will usually sleep for a few hours).

We try not to overstimulate her, we keep it comfortable but boring (and make day time fun and bright to help her circadian rhythms).

We know that four week olds don't really have a 'routine' per se, it's just very annoying that her peak awake time is at such an inconvenient time of day and living on 3.5 hours sleep is killing me.

Does anyone have any tricks to help us help her get back to sleep after her feed?

As an inexperienced parent of a three week old, there are probably more reliable opinions out there, but have you tried swaddling with lots of movement around the room, putting on a sling and walking around the room, music or white noise?

Lots of walking around and jiggling her in your arms

That's how mine was as a very small baby. Go to bed early in the evening and grab what sleep you can while she's asleep. It'll pass.

Thanks guys and Spicy great idea, that's exactly how we get her off to sleep in the first place (tightly wrapped, jiggling, on the move) - so OF COURSE it makes sense to do the same to get her back to sleep. I'd either discounted it because I didn't want to over stimulate her or I'd forgotten it because we're so damn tired... But tonight we try it!

Thank you all!

Dummy usually helps