We introduce a novel method for numerical spin glass investigations: S
imulations of two replica at fixed temperature, weighted to achieve a
broad distribution of the Parisi overlap parameter q (multioverlap). W
e demonstrate the feasibility of the approach by studying the 3D Edwar
ds-Anderson Ising (J(ik) = +/-1) spin glass in the broken phase (beta
= 1). This makes it possible to obtain reliable results about spin gla
ss tunneling barriers. In addition, our results indicate a nontrivial
scaling behavior of the canonical q distributions not only at the free
zing point but also deep in the broken phase.