  We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram
contains a unique dotted edge. We prove that such a polytope in d-dimensional
hyperbolic space has at most d+3 facets. In view of results of Lann\'er,
Kaplinskaja, Esselmann, and the second author, this implies that compact
hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are
completely classified. They do exist only up to dimension 6 and in dimension 8.
