Matroid 3-connectivity and branch width

We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the branch width of M is sufficiently large, then there is a k  -element set X⊆E(M)X⊆E(M) such that one of M\XM\X and M/XM/X is 3-connected and contains N as a minor.