Martin:

That's true. But it is even better. Unless the Higgs has pretty much exactly 116 GeV, so called loop corrections will destroy the model once more, if there are not more particles to shield these effect. As this is a kind of fine tuning people are not heavy with it, there are basically two classes of models introducing new particles.

Is that "kind of fine tuning" a fixed point of the renormalization group flow? Because, in that case, there's nothing particularly bothersome about the fine tuning: it's an internally dynamically-determined parameter of the model, not an externally finely-tuned parameter.

We have met the enemy, and he is us — Pogo