In a companion paper as well as in earlier publications, it has been shown that in asymmetric frame buildings, designed in accordance with modern codes and subjected to strong earthquake excitations, the ductility demands at the so called "flexible" edges are consistently and substantially higher than the ductility demands at the "stiff" edges of the building. In some cases the differences in the computed ductility factors between elements at the two opposite building edges exceeded 100%. Similar findings have also been reported for code designed reinforced concrete buildings. This is an undesirable behavior as it indicates no good use of material and the possibility for overload of the "flexible" edge members with a consequent potential for premature failure. In the present paper, a design modification will be introduced that can alleviate the problem and lead to a more uniform distribution of ductility demands in the elements of all building edges. The presented results are based on the steel frames detailed in the companion paper. This investigation is another step towards more rational design of non-symmetric steel buildings.