I have seen many examples of universal Turing machines, all of which are undecidable due to the undecidability of the halting problem. I have also seen proofs that certain really small Turing machines are decidable and therefore not universal. I have also seen Turing machines that provably do simple enough calculations that they are not universal. It seems that every Turing machine is either complex enough to be universal or simple enough to be decidable.
My question is if there is a Turing machine that lives on this line, namely, is undecidable but provably not universal? (Related question: How would you even prove that such a machine was not universal under those conditions?)