T-parity, its problems and their solution

We point out a basic difficulty in the construction of little-Higgs models with T-parity which is overlooked by large part of the present literature. Almost all models proposed so far fail to achieve their goal: they either suffer from sizable electroweak corrections or from a breakdown of collective breaking. We provide a model building recipe to bypass the above problem and apply it to build the simplest T-invariant extension of the Littlest Higgs. Our model predicts additional T-odd pseudo-Goldstone bosons with weak scale masses.