  We give a direct proof of the local $Tb$ Theorem, in the Euclidean setting,
and under the assumption of dual exponents. This Theorem provides a flexible
framework for proving the boundedness of a Calder\'on-Zygmund operator,
supposing the existence of systems of local accretive functions. We assume that
the integrability exponents on these systems of functions are of the form
$1/p+1/q\le 1$, and provide a direct proof. The principal point of interest is
in the use of random grids and the corresponding construction of the corona. We
also utilize certain twisted martingale transform inequalities.
