Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) reconstructibility analysis, is presented. It is shown that in some cases, while three-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using MRA. Also, it is shown that whenever a decomposition of three-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions and MRA is also presented. While both AC and MRA decompose some but not all NPN-classes, MRA decomposes more classes, and consequently more Boolean functions. MRA for many-valued functions is also presented, and algorithms using two different methods (intersection and union) are given. A many-valued case is presented where CRA fails to decompose but MRA decomposes.