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Suppose M is a closed irreducible orientable 3-manifold, K is a knot in M, Pand Q are bridge surfaces for K and K is not removable with respect to Q. Weshow that either Q is equivalent to P or $d(K,P) \leq 2-\chi(Q-K)$. If K is nota two bridge knot, then the result holds even if K is removable with respect toQ. As a corollary we show that if a knot in the 3-sphere has high distance withrespect to some bridge sphere and low bridge number, then the knot has a uniqueminimal bridge position.

Multiple bridge surfaces restrict knot distance