I've been reading more about sleep, and I think the "your baby needs to learn how to fall asleep on their own" people are right. She can go to sleep when we bounce her on our shoulder, or pat her stomach, or bounce the crib mattress a bit, but she can't just fall asleep on her own. It looks like at her age most babies can, and "my baby wakes up in the night and needs to be put rocked to sleep" seems to one of the most common sleep problems. So I think we should be putting her to bed and letting her fall asleep, and then if after N minutes she's not asleep picking her up, comforting her, and putting her back down. We could start with N=5 and then slowly lengthen it. I think we should start this soon, probably tonight. She's not sleeping well as it is, we're not either, and we don't want her expectation that we will comfort her back to sleep to get stronger.

Julia thought that if we tried this Lily would probably learn to fall asleep on her own, but that it would be very painful for all of us while she learned. Occasionally we had tried leaving Lily to cry for a few minutes to see whether she calmed down, and her cries tended to escalate and keep escalating. And reading things like this made me very nervous:

For an hour and forty-five minutes every night we tried, Wood fled outdoors to walk halfway from the Ocean to the Bay and I paced through our one-bedroom apartment, searching for some audial deadspot to escape her screams but I couldn't. It's just too small. Her screams were everywhere. And they didn't stop like Weissbluth said they eventually would. They just never stopped. —Sweet Juniper

While cry-it-out still seemed like something we might try at some point, it seemed to me that the real problem is that the environment in which Lily was going from awake to asleep was different than the one in which she would wake up. Falling asleep one of us would be there, patting or bouncing her, but when she woke up she would be on her own. So I decided to try something else. During my turns putting her to sleep, where I had previously been patting her until she was well asleep I switched to stopping as soon as she stopped crying. Several times in a row she would start crying, I would pat her stomach, she would stop, I would stop, and we'd begin again. But then she would close her eyes and go to sleep, on her own, without any touch or movement! It seemed she was learning to fall herself asleep.

Over the next few days Lily got better and better at falling back to sleep on her own when she woke up a bit at the end of a sleep cycle. It's been almost two weeks now, and while she's still not sleeping as well as we'd like she's been doing much better. The last couple nights she's woken twice to feed and otherwise has put herself back to sleep after one or two quiet cries.

So: I've been trying this for a couple weeks and it seems a lot better, but it's hard to know whether this is regression to the mean, Lily getting older and more competent, or actually something that worked.