  We consider a class of little Higgs theories with T-parity where ALL new
particles responsible for canceling the standard model contributions to the
one-loop quadratic divergences in the Higgs potential are odd under T-parity,
including the heavy top partner which was previously taken to be T-even. The
new construction significantly simplifies the spectrum in the top sector and
completely changes the phenomenology of the top partner. At hadron colliders
the signals of this class of T-invariant models appear to be even more similar
to supersymmetry. We initiate a study on the collider phenomenology and discuss
the challenge of distinguishing this class of models from supersymmetry at the
Large Hadron Collider.
