How long has this gone on? My initial thought is that if it is a pretty recent thing, it may be a growth spurt, and just go with it for a week or two. However, if it has been going on for months, I think it is just a habit your baby has gotten into. There is a difference between wanting or expecting to eat, and actually needing to eat. For instance, most of the time, when we wake up in the middle of the night, we could eat, right? But we know enough to just roll over and go back to sleep. Maybe your baby has more of a problem getting back to sleep rather than being that hungry. At 11 months, she should comfortably go at least 10-11 hours before waking to eat. I know it sounds silly, but try pushing her bedtime earlier by an hour or so to see if that helps her sleep later. Also, I liked the idea of decreasing the amount of milk each night, until you just go in to soothe her when she wakes. Set a time in the AM that you won't feed her before, and stick to it. Soothe her back to sleep any way you need to. Just some thoughts--best of luck!