New sets of parameter tunes for two of the colour reconnection models, quantum chromodynamics-inspired and gluon-move, implemented in the PYTHIA 8 event generator, are obtained based on the default CMS PYTHIA 8 underlying-event tune, CP5. Measurements sensitive to the underlying event performed by the CMS experiment at centre-of-mass energies root s = 7 and 13 TeV, and by the CDF experiment at 1.96 TeV are used to constrain the parameters of colour reconnection models and multiple-parton interactions simultaneously. The new colour reconnection tunes are compared with various measurements at 1.96, 7, 8, and 13 TeV including measurements of the underlying-event, strange-particle multiplicities, jet substructure observables, jet shapes, and colour flow in top quark pair (t (t) over bar) events. The new tunes are also used to estimate the uncertainty related to colour reconnection modelling in the top quark mass measurement using the decay products of t (t) over bar events in the semileptonic channel at 13 TeV.