  We investigate the theoretical description of the central exclusive
production process, $h_1 + h_2 \to h_1+X+h_2$. Taking Higgs production as an
example, we compute the subset of next-to-leading order corrections sensitive
to the Sudakov factor appearing in the process. Our results agree with those
originally presented by Khoze, Martin and Ryskin except that the scale
appearing in the Sudakov factor, $\mu=0.62 \sqrt{\hat{s}}$, should be replaced
with $\mu=\sqrt{\hat{s}}$, where $\sqrt{\hat{s}}$ is the invariant mass of the
centrally produced system. We show that the replacement leads to approximately
a factor 2 suppression in the cross-section for central system masses in the
range 100--500GeV.
