  The unknotting number $u$ and the genus $g$ of braid positive knots are
equal, as shown by Rudolph. We prove the stronger statement that any positive
braid diagram of a genus $g$ knot contains $g$ crossings, such that changing
them produces a diagram of the trivial knot. Then, we turn to unknotting the
more general class of fibered positive knots, for which $u = g$ was conjectured
by Stoimenow. We prove that the known ways to unknot braid positive knots do
not generalize to fibered positive knots. Namely, we prove that there are
fibered positive knots that cannot be unknotted optimally along fibered
positive knots; there are fibered positive knots that do not arise as trefoil
plumbings; and there are positive diagrams of fibered positive knots of genus
$g$ that do not contain $g$ crossings, such that changing them produces a
diagram of the trivial knot. In fact, we conjecture that one of our examples is
a counterexample to Stoimenow's conjecture.
