For 24 long hours, every time she was put on her back she would flip over. At this point she had two choices: she could hold her head up, or put it on the ground. She seemed to miss the fact that she could turn her head in order to lie on her cheek. To make a difficult situation even more complicated, she is more prone to spit-up when she is on her belly. So she could not be put down to sleep unless she was completely asleep.
The first night she could turn over on her own was one of the few nights that she didn't go immediately back to sleep after nursing. So we had to put her in her swing. Where she spent the next long while cooing, laughing, and squealing with delight. As pleasant as those sounds normally are, they lose some of their allure at 4 am.
The next day she learned to turn her head. The problems are not solved, but they are at least lessened. That is not sweat on her head, but spit-up in her hair. Lovely.