Flotsam & Jetsam ad a song (before I was born) that went
Is he an Ozzie, Lizzie, is he?

Not sure if thsi qualifies as a TT:
Around the rugged rock the ragged rascal ran
(Not for Jonathan Ross, that one)

And this one isn't a TT, but, like the pheasant plucker, it tends to change when you say it out loud:
I chased a bug around a tree; I'll have his blood, he knows I will

Steve