  A local Tb Theorem provides a flexible framework for proving the boundedness
of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator
T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes.
We give a new proof of this Theorem in the setting of perfect (dyadic) models
of Calder\'on-Zygmund operators, imposing integrability conditions on the b_Q
functions that are the weakest possible. The proof is a simple direct argument,
based upon a new inequality for transforms of so-called twisted martingale
differences.
