The grid vision of a single computing utility has yet to materialize: while many grids with thousands of processors each exist, most work in isolation. An important obstacle for the effective and efficient inter-operation of grids is the problem of resource selection. In this paper we propose a solution to this problem that combines the hierarchical and decentralized approaches for interconnecting grids. In our solution, a hierarchy of grid sites is augmented with peer-to-peer connections between sites under the same administrative control. To operate this architecture, we employ the key concept of delegated matchmaking, which temporarily binds resources from remote sites to the local environment. With trace-based simulations we evaluate our solution under various infrastructural and load conditions, and we show that it outperforms other approaches to inter-operating grids. Specifically, we show that delegated matchmaking achieves up to 60% more goodput and completes 26% more jobs than its best alternative.