You're not wrapping them tight enough if a 3 week old is able to squirm out. Work on making it tighter and making sure you really tuck it underneath them with the last wrap and they should be unable to work their way loose.
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Agreed - our second boy loved to wiggle his arms out; just had to figure out a good approach to wrapping the arm first and then wrapping that side over the body.
Nothing is fool proof, but it will generally hold for a nap or the next dirty diaper :)
Im not sure if this is the exact brand, but this is the style we use cause our kids all busted out and all wanted to sleep with their arms up around their heads.
I second this one. Worked well for our son as he seemed to like sleeping with his arms up and out. He's 4.5 months now and we've transitioned into the Merlin sleep suit since he still likes having his arms somewhat free to hold his pacifier as he sleeps.
Thirded! Also worked for us in a car seat.
Get the velcro swaddles, like SwadleMe, and when swaddling hold their arms straight at their sides while you wrap tight like a burrito. You should be able to keep them swaddled until at least 3 months. From there we moved on to a sleep sack.
We liked the Nested Bean swaddles, with the arms that can be unzipped when they get older. But sometimes it takes some experimenting to determine what works best for your baby.
I'm going to give you permission to not swaddle. Swaddles aren't necessary. At three weeks old there is nothing but a rough night. They don't have stomachs large enough to tank up on calories to sleep for large periods of time. Small tummy = frequent wake = frequent feed. Moro helps prevent SIDS so don't hate on it.