  We consider the central exclusive production of high $E_T$ jets $pp\to
p+(X+{\rm dijet})+p$. In particular we study the possible contamination of the
purely exclusive signal by semi-exclusive production where no other secondaries
are emitted in one hemisphere, between the highest $E_T$ dijet and the recoil
proton, while in the other hemisphere a third jet, plus possibly additional
hadron activity, is allowed, but still separated from the incoming proton by a
large rapidity gap. This process arising from the fusion of a hard and a soft
Pomeron has not been considered before. It turns out that it gives a negligible
contribution. %contamination, which was not known before the calculation. The
calculation involves a careful treatment of the QCD colour structure of the
amplitudes.
