Fist sucker???

MJ has a need to be sucking on something for most of the day, but she won't take a pacifier to save her life. I have tried several different kinds, but she just makes faces and gags on them and spits them out. She will occasionally suck on someone's finger or knuckle, but one can only do that for so long. Lately she has started sucking on her fist and it doesn't matter which hand. Sometimes she will get almost the whole fist in her mouth and be sucking away - rather noisily too...