  We present precise predictions for four-lepton plus jets production at the
LHC obtained within the fully automated Sherpa+OpenLoops framework. Off-shell
intermediate vector bosons and related interferences are consistently included
using the complex-mass scheme. Four-lepton plus 0- and 1-jet final states are
described at NLO accuracy, and the precision of the simulation is further
increased by squared quark-loop NNLO contributions in the gg -> 4l, gg -> 4l+g,
gq -> 4l+q, and qq -> 4l+g channels. These NLO and NNLO contributions are
matched to the Sherpa parton shower, and the 0- and 1-jet final states are
consistently merged using the MEPS@NLO technique. Thanks to Sudakov
resummation, the parton shower provides improved predictions and uncertainty
estimates for exclusive observables. This is important when jet vetoes or jet
bins are used to separate four-lepton final states arising from Higgs decays,
diboson production, and top-pair production. Detailed predictions are presented
for the ATLAS and CMS H->WW analyses at 8 TeV in the 0- and 1-jet bins.
Assessing renormalisation-, factorisation- and resummation-scale uncertainties,
which reflect also unknown subleading Sudakov logarithms in jet bins, we find
that residual perturbative uncertainties are as small as a few percent.
