  We relate two conjectures that play a central role in the reported proof of
Rota's Conjecture. Let $\mathbb F$ be a finite field. The first conjecture
states that: the branch-width of any $\mathbb F$-representable $N$-fragile
matroid is bounded by a function depending only upon $\mathbb F$ and $N$. The
second conjecture states that: if a matroid $M_2$ is obtained from a matroid
$M_1$ by relaxing a circuit-hyperplane and both $M_1$ and $M_2$ are $\mathbb
F$-representable, then the branch-width of $M_1$ is bounded by a function
depending only upon $\mathbb F$. Our main result is that the second conjecture
implies the first.
