This paper discusses ways of reducing fragmentation ion in buddy systems. Although internal fragmentation may be estimated for any buddy system, external fragmentation cannot be determined theoretically. It is suggested here that mean external fragmentation for any buddy system is directly related to the height of the associated binary tree. Simulation studies with a new buddy system support this conjecture. Attempts at reducing internal fragmentation have, in the past, increased the tree height covering the range of request sizes and given rise to a commensurate increase in external fragmentation. A new buddy system is described which supports a large number of buddy sizes without requiring a large tree height. The new scheme is a modified form of the weighted buddy method, entitled the dual buddy system. It provides the same set of block sizes as the weighted scheme but has the same tree height as the binary buddy system. Simulation results show that mean external fragmentation is within four percent of that of the binary system and much lower than that of the weighted scheme. The new system has better overall storage utilization han others for uniform random request sizes.