A central finding in dialogue research is that interlocutors rapidly converge on referring expressions which become progressively contracted and abstract. However there is currently no consensus on which mechanisms underpin convergence: The interactive alignment model (Pickering and Garrod, 2009) favours alignment processes, the grounding model (Clark, 1996) prioritizes positive feedback, while Healey (2002) demonstrates the importance of miscommunication in identifying differences of interpretation. To investigate convergence we report a variant of the maze-task in which both participants are given misaligned instructions: One participant is primed with instructions that conceptualize the maze as consisting of horizontal vectors (e.g ."4th row, 2nd square"); the other is primed with instructions that conceptualize the maze as consisting of vertical vectors (e.g ."3rd column, 2nd square"). Compared with a baseline, misaligned dyads converged on more abstract referring expressions. We argue this pattern is due to participants interactively combining their perspective with that of their partner.