  A resolution $Z \to X$ of a Poisson variety $X$ is called {\em Poisson} if
every Poisson structure on $X$ lifts to a Poisson structure on $Z$. For
symplectic varieties, we prove that Poisson resolutions coincide with
symplectic resolutions. It is shown that for a Poisson surface $S$, the natural
resolution $S^{[n]} \to S^{(n)}$ is a Poisson resolution. Furthermore, if
$Bs|-K_S| = \emptyset$, we prove that this is the unique projective Poisson
resolution for $S^{(n)}$.
