  The average lifetime ($\tau(H)$) it takes for a randomly started trajectory
to land in a small region ($H$) on a chaotic attractor is studied. $\tau(H)$ is
an important issue for controlling chaos. We point out that if the region $H$
is visited by a short periodic orbit, the lifetime $\tau(H)$ strongly deviates
from the inverse of the naturally invariant measure contained within that
region ($\mu_N(H)^{-1}$). We introduce the formula that relates
$\tau(H)/\mu_N(H)^{-1}$ to the expanding eigenvalue of the short periodic orbit
visiting $H$.
