Since Steven is no longer sleeping through the night, I haven't fully tested them, but I LOVE Huggies Supreme Ultra Care. They are much thicker than the Pampers Swaddlers and seem a ton more absorbant. I forgot to change him while we were out the other day (for a really long time), and the diaper was huge, but it didn't leak. Yay!
I also bought some lap pads to put under him when he sleeps. So far I haven't had to use them.
Thanks for all your great advice. (BTW, Huggies Overnights start at size 3, but we'll probably try them when we get there!)