The authors consider the partitioning of a problem on a domain with unequal work estimates in different subdomains in a way that balances the work load across multiple processors. Such a problem arises, for example, in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. A binary decomposition of the domain to partition it into rectangles requiring equal computational effort is used. The communication costs of mapping this partitioning onto a tree machine and a mesh-connected array are analyzed. The communication cost can be used to determine the optimal depth of this partitioning.