Concurrent requests to a shared variable by many processors on a shared memory machine can create contention that will be serious enough to stall large machines. This idea has been formalized in the “hot spot” traffic [PfNo85], where a fixed fraction of memory requests is for a single shared variable. “Combining”, in which several requests for the same variable can be combined into a single request, has been suggested as an effective method of alleviating the contention. Lee, Kruskal, and Kuck [LeKK86] introduced the idea of “k-way combining”, which shows that the effectiveness of combining depends on k, the maximum possible number of requests combined into a single request at a switch. This paper introduces a scheme to remedy k-way combining in order to avoid the contention without incurring impractically large storages in switches of multistage interconnection networks.