New sets of parameters (“tunes”) for the underlying-event (UE) modelling of the pythia8, pythia6 and herwig++ Monte Carlo event generators are constructed using different parton distribution functions. Combined fits to CMS UE proton–proton ( $\mathrm {p}\mathrm {p}$ ) data at $\sqrt{s} = 7,\text {TeV} $ and to UE proton–antiproton ( $\mathrm {p}\overline{\mathrm{p}} $ ) data from the CDF experiment at lower $\sqrt{s}$ , are used to study the UE models and constrain their parameters, providing thereby improved predictions for proton–proton collisions at 13 $,\text {TeV}$ . In addition, it is investigated whether the values of the parameters obtained from fits to UE observables are consistent with the values determined from fitting observables sensitive to double-parton scattering processes. Finally, comparisons are presented of the UE tunes to “minimum bias” (MB) events, multijet, and Drell–Yan ( $ \mathrm{q} \overline{\mathrm{q}} \rightarrow \mathrm{Z}/ \gamma ^* \rightarrow $ lepton-antilepton+jets) observables at 7 and 8 $,\text {TeV}$ , as well as predictions for MB and UE observables at 13 $,\text {TeV}$ .