  Meson-meson correlation effects are investigated in the $\NNb\to\rho\pi$
annihilation process using a realistic meson-exchange model for the $\rho\pi$
interaction determined previously, together with a conventional baryon-exchange
transition model and a consistent $\NNb$ interaction. For $\NNb$ $S$-states,
they have a drastic effect and bring the relative (${^1S_0}/{^3S_1}$) branching
ratio up to the experimental value, thus resolving the long-standing so-called
``$\rho\pi$'' puzzle. For $\NNb$ $P$-states, their effect is of minor
importance, and discrepancies remain for those ratios involving annihilation
from the $\NNb({^3P_J})$ state to $\rho\pi(l'=2)$.
