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The problem of finding the closest lattice point arises in several communications scenarios and is known to be NP-hard. We propose a new closest lattice point search algorithm which utilizes a set of new linear inequality constraints to reduce the search of the closest lattice point to the intersection of a polyhedron and a sphere. This set of linear constraints efficiently leverage the geometric structure of the lattice to reduce considerably the number of points that must be visited. Simulation results verify that this algorithm offers substantial computational savings over standard sphere decoding when the dimension of the problem is large.