  We prove an effective form of Wilkie's conjecture in the structure generated
by restricted sub-Pfaffian functions: the number of rational points of height
$H$ lying in the transcendental part of such a set grows no faster than some
power of $\log H$. Our bounds depend only on the Pfaffian complexity of the
sets involved. As a corollary we deduce Wilkie's original conjecture for
$\mathbb{R}_{\mathrm{exp}}$ in full generality.
