I know you can't really sleep train a 5 week old, but....

Ashley
Do any of you have experience with the best way to let a 5 week old resettle at night? Like most babies, my girl sleeps better on my chest, in my arms or in her swing, but I want to make sure she learns to sleep fine on her back in her bassinet. But when I lay her flat on her back she only stays calm and asleep anywhere from 1 minute to an hour (at night that's no good because she can usually sleep 4.5 hours straight).
I have a problem with picking her up right when she she starts to fuss (I can't stand her being unhappy and just want to hold her!)... I'm wondering how long I should let her fuss before I try to resettle her. I've assumed I should do it before she starts really crying because then I feel like she wakes herself up even more! Advice?