We consider the inclusion and equivalence problem for unambiguous Büchi automata. We show that for a strong version of unambiguity introduced by Carton and Michel these two problems are solvable in polynomial time. We generalize this to Büchi automata with a fixed finite degree of ambiguity in the strong sense. We also discuss the problems that arise when considering the decision problems for the standard notion of ambiguity for Büchi automata.