  We present results of recent high-statistics Monte Carlo simulations of the
Edwards-Anderson Ising spin-glass model in three and four dimensions. The study
is based on a non-Boltzmann sampling technique, the multi-overlap algorithm
which is specifically tailored for sampling rare-event states. We thus
concentrate on those properties which are difficult to obtain with standard
canonical Boltzmann sampling such as the free-energy barriers F^q_B in the
probability density P_J(q) of the Parisi overlap parameter q and the behaviour
of the tails of the disorder averaged density P(q) = [P_J(q)]_av.
