binky baby

Savanna is obsessed with her binkys.  I have only been letting her have them in her crib, but she seems to find them or convince her sister to get her one every time I turn around!  When she can't find one, she starts sucking her thumb or fingers--which I think is even worse!!  The other day she was playing with the doll that has a binky.  Before I knew it, she had the doll binky in her mouth!  It was so funny.  We are going to have to break the binky habit soon because I have a feeling she will be taking the her new little sister's binky out of her mouth constantly if we don't wean her off of them soon!  I just don't want her sucking her fingers or thumb...what dilemma.