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 $$\,\text {TeV}$$ .