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This paper proposes a new class of simple, distributed algorithms for scheduling in multihop wireless networks under the primary interference model. The class is parameterized by integers k ges 1. We show that algorithm k of our class achieves k/(k + 2) of the capacity region, for every k ges 1. The algorithms have small and constant worst-case overheads. In particular, algorithm k generates a new schedule using a) time less than 4k + 2 round-trip times between neighboring nodes in the network and b) at most three control transmissions by any given node for any k. The control signals are explicitly specified and face the same interference effects as normal data transmissions. Our class of distributed wireless scheduling algorithms are the first ones guaranteed to achieve any fixed fraction of the capacity region while using small and constant overheads that do not scale with network size. The parameter k explicitly captures the tradeoff between control overhead and throughput performance and provides a tuning-knob protocol designers can use to harness this tradeoff in practice.