  The recently published data for $<p^2_t>$ for $J/\psi$ production in Pb-Pb
collisions at 158 A GeV are analyzed. For low values of transverse energy
$E_t$, where normal suppression dominates, $<p^2_t> (E_t)$ scales with the path
length of the gluons which fuse to make the $J/\psi$. In the $E_t$ domain of
anomalous suppression $<p^2_t> (E_t)$ is found to rise linearly with the
relative amount of anomalous suppression. This empirical law is reproduced
within an analytically solvable transport model which allows high $p_t$
$J/\psi$'s to escape anomalous suppression. Interpreted in this way, the data
for $<p^2_t> (E_t)$ lead to an estimate of $t_A \sim 4$ fm/$c$ for the duration
of anomalous suppression.
