  Recently, a method has been proposed to obtain accurate predictions for
low-temperature properties of lattice spin glasses that is practical even above
the upper critical dimension, $d_c=6$. This method is based on the observation
that bond-dilution enables the numerical treatment of larger lattices, and that
the subsequent combination of such data at various bond densities into a
finite-size scaling Ansatz produces more robust scaling behavior. In the
present study we test the potential of such a procedure, in particular, to
obtain the stiffness exponent for the hierarchical Migdal-Kadanoff lattice.
Critical exponents for this model are known with great accuracy and any
simulations can be executed to very large lattice sizes at almost any bond
density, effecting a insightful comparison that highlights the advantages -- as
well as the weaknesses -- of this method. These insights are applied to the
Edwards-Anderson model in $d=3$ with Gaussian bonds.
