  We point out that in decays of the type $B^- \to D^* K^-$, where the neutral
$D^*$ meson is an admixture of $D^{*0}$ and $\bar{D}^{*0}$, there is an
effective strong phase difference of $\pi$ between the cases that the $D^*$ is
reconstructed as $D\pi^0$ and $D\gamma$. We consider the consequences for
measurements of $\phi_3$ using these modes, some of which are profound and
beneficial.
