Pull the other one, it's got bells on

Can someone help me with the ORIGIN of THIS expression?
I'm not looking for it's meaning, I know it's when someone doesn't believe what was said. I'm not looking for the origin of Pulling my leg either - just the phrase Pull The Other One, It's Got Bells On.
BTW - what is the connection between the bells and someone's leg? Doesn't seem relevant, just two expressions that got confused together.

Dictionary of Catch Phrases: American and British, from the Sixteenth Century to the Present Day, by Eric Partridge, has an entry for this phrase. It says just a little about the origin: "Frank Shaw attributed it to the 1920s" (no, I don't know who he was) and "Presumably from pictures of court jesters, wearing cap and bells."

I thought it was older than that. This explanation doesn't make sense, is there a chance for a better one?