  It has been shown recently that the introduction of an unphysical
$\epsilon$-scalar mass $\tilde{m}$ is necessary for the proper renormalization
of softly broken supersymmetric theories by dimensional reduction ($\drbar$).
In these theories, both the two-loop $\beta$-functions of the scalar masses and
their one-loop finite corrections depend on $\tilde{m}^2$. We find, however,
that the dependence on $\tilde{m}^2$ can be completely removed by slightly
modifying the \drbar renormalization scheme. We also show that previous \drbar
calculations of one-loop corrections in supersymmetry which ignored the
$\tilde{m}^2$ contribution correspond to using this modified scheme.
