This paper designs a new equalization-aid formula based on fiscal gaps of local communities. When states are in transition to a new local aid formula, the issue of whether and how to hold existing aid harmless poses a challenge. The authors show that some previous studies and the formulas derived from them give differential weights to existing and new aid in filling the gap and hence effectively treat communities receiving greater amounts of existing aid more favorably than communities receiving less or no existing aid. As a fairer alternative, the authors propose a new approach that considers existing and new aid as completely equivalent in filling the gap by focusing on the equalizing impact of combined (new and existing) aid. In addition, unlike most previous research that focuses only on a single year's new aid distribution, the authors simulate the dynamics of aid distributions over multiple years using Massachusetts data. They further provide and compare several possible methods by which state policymakers could direct extra aid dollars to communities with larger unfilled gaps in dollar terms. Although the proposed aid formula is designed for municipal aid and tailored to Massachusetts, the authors note that foundation aid formulas for education implicitly treat existing aid in the same way and suggest that the framework, principles, and policy recommendations might also be applicable to other states. (Contains 4 figures, 4 tables and 26 footnotes.)