We present a new, universally applicable toy model of colour reconnections in hadronic final states. The model is based on hadronising strings and has one free parameter. We next present an implementation of this model in the PYTHIA event generator and provide several parameter sets ('tunes'), constrained by fits to Tevatron minimum-bias data. Finally, we consider the sensitivity of a simplified top mass analysis to these effects, in exclusive semi-leptonic top events at the Tevatron. A first attempt at isolating the genuine non-perturbative effects gives an estimate of order δmtop ∼ ±0.5 GeV from non-perturbative uncertainties, and a further δmtop ∼ ±1 GeV from shower effects.