  We report large-scale simulations of the three-dimensional Edwards-Anderson
Ising spin glass system using the recently introduced multi-overlap Monte Carlo
algorithm. In this approach the temperature is fixed and two replica are
coupled through a weight factor such that a broad distribution of the Parisi
overlap parameter $q$ is achieved. Canonical expectation values for the entire
$q$-range (multi-overlap) follow by reweighting. We present an analysis of the
performance of the algorithm and in particular discuss results on spin glass
free-energy barriers which are hard to obtain with conventional algorithms. In
addition we discuss the non-trivial scaling behavior of the canonical
$q$-distributions in the broken phase.
