Many Higgs analyses divide the data into exclusive jet bins since the background decomposition changes considerably depending on the number of jets in the final state. In this talk we present our work on exclusive Higgs+jet production via gluon fusion, with a veto on additional jets. We perform the resummation of jet-veto logarithms to NNLL′ accuracy, using a different factorization theorem than previous theory predictions for this process. We match the resummed cross section to the NNLO fixed order result, and treat unknown quantities as theory nuisance parameters