We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N = 1 supersymmetric theory. Regularization by dimensional reduction respects supersymmetry, but standard dimensional regularization does not. We find expressions for the differences between running couplings in the modified minimal subtraction schemes of these two regularization methods, to one-loop order. We also find the two-loop renormalization group equations for gaugino masses in both schemes, and discuss the application of these results to the Minimal Supersymmetric Standard Model.