We explore how the inclusion of an anti-trapping current within a phase-field model of coupled thermo-solutal growth formulated in the thin interface limit actually affects the observed levels of solute trapping during dendritic growth. The problem is made computationally tractable by the use of advanced numerical techniques including local mesh adaptivity, implicit temporal discretization and a multigrid solver. Contrary to published results for pure solutal models we find that the inclusion of such an anti-trapping current does not lead to the recovery of the equilibrium partition coefficient, except in the limit of vanishing growth velocity. At higher growth velocities non-vanishing amounts of solute trapping are observed. (C) 2010 Elsevier B.V. All rights reserved.