Bridging separations in matroids

Let (X-1, X-2) be an exact k-separation of a matroid N. If M is a matroid that contains N as a minor and the k-separation (X-1, X-2) does not extend to a k-separation in M, then we say that M bridges the k- separation (X-1, X-2) in N. One would hope that a minor minimal bridge for (X-1, X-2) would not be much larger than N. Unfortunately there are instances in which one can construct arbitrarily large minor-minimal bridges. We restrict our attention to the class of matroids representable over a fixed finite field and show that here minor-minimal bridges are bounded in size.