  For the Edwards-Anderson Ising spin-glass model in three and four dimensions
(3d and 4d) we have performed high statistics Monte Carlo calculations of those
free-energy barriers $F^q_B$ which are visible in the probability density
$P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the
recently introduced multi-overlap algorithm. In both dimensions, within the
limits of lattice sizes investigated, these barriers are found to be
non-self-averaging and the same is true for the autocorrelation times of our
algorithm. Further, we present evidence that barriers hidden in $q$ dominate
the canonical autocorrelation times.
