  Ito-Takimura recently defined a splice-unknotting number $u^-(D)$ for knot
diagrams. They proved that this number provides an upper bound for the crosscap
number of any prime knot, asking whether equality holds in the alternating
case. We answer their question in the affirmative. (Ito has independently
proven the same result.) As an application, we compute the crosscap numbers of
all prime alternating knots through at least 13 crossings, using Gauss codes.
