2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104792Suppose M is a closed irreducible orientable 3-manifold, K is a knot in M, P and Q are bridge surfaces for K and K is not removable with respect to Q. We show that either Q is equivalent to P or $d(K,P) \leq 2-χ(Q-K)$. If K is not a two bridge knot, then the result holds even if K is removable with respect to Q. As a corollary we show that if a knot in the 3-sphere has high distance with respect to some bridge sphere and low bridge number, then the knot has a unique minimal bridge position.47 pages, 16 figures, references and figures added, the main result has been slightly strengthenedGeometric Topology57M25, 57M27, 57M50text