  We show that the $L^2(w)$ operator norm of the composition $M\!\circ
T_{\Omega}$, where $M$ is the maximal operator and $T_{\Omega}$ is a rough
homogeneous singular integral with angular part $\Omega\in
L^{\infty}(S^{n-1})$, depends quadratically on $[w]_{A_2}$, and this dependence
is sharp.
