Anything Muppets: A sticky subject

[lowercasegods]

My girlfriend brought up an interesting question last night: In the case of "anything" Muppets, such as those which frequently have their eyes, nose, ears, hair or whatever changed around to suit a new character, what do they use to apply these new pieces to the puppets? When I was a kid I assumed it was velcro that would adhere a new set of eyes and a nose to a puppet, for example, turning Mumford into the Count. But we've seen Ernie pull Bert's nose off his face with no visible sign of velcro. It's possible that glue is used, but the glue couldn't be that strong if a nose could be popped right off, meaning the feature couldn't easily sit on the puppet's face because the glue is too weak. And the glue couldn't be that weak, since these items do seem to rest securely on the faces. So what exactly is used to hold these pieces on and then make them easy to remove? This is a question that's long overdue for me to ask, so if anyone knows, I'd appreciate the info.