We present results of high-statistics Monte Carlo simulations of the three-dimensional Edwards--Anderson Ising spin-glass model. The study is performed with the multi-overlap algorithm, a non-Boltzmann sampling technique which is specifically tailored for sampling rare-event states. This enabled us to study the free-energy barriers F^q_B in the probability densities P_J(q) of the Parisi overlap parameter q and the far tail region of the disorder averaged density P(q) = [P_J(q)]_av. In the latter case we find support for extreme order statistics over many orders of magnitude. A comparative study of the three-dimensional pure Ising model shows that this property is special to spin glasses.

PACS numbers: 75.10.Nr, 75.40.Mg, 75.50.Lk