  The modelling of non-perturbative effects is an important part of modern
collider physics simulations. In hadron collisions there is some indication
that the modelling of the interactions of the beam remnants, the underlying
event, may require non-trivial colour reconnection effects to be present. We
recently introduced a universally applicable toy model of such reconnections,
based on hadronising strings. This model, which has one free parameter, has
been implemented in the Pythia event generator. We then considered several
parameter sets (`tunes'), constrained by fits to Tevatron minimum-bias data,
and determined 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 gave an estimate of order
+-0.5GeV from non-perturbative uncertainties. The results presented here are an
update to the original study and include recent bug fixes of Pythia that
influenced the tunings investigated.
