  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.
