Natural language dialogue between multiple participants re-quires conversational grounding, a process whereby interlocu-tors achieve a shared understanding. However, the mecha-nisms involved in the grounding process are under dispute.Two prominent models of dialogue between multiple partici-pants are: interactive alignment, a simpler model that relieson automatic priming processes within individuals, and in-terpersonal synergy, a more complicated model emphasizingcoordinated interaction across participants. Using recurrenceanalysis methods, Fusaroli and Tyl ́en (2016) simultaneouslyevaluated both models and showed that alignment is an insuf-ficient explanation for grounding or for the teams’ task per-formance. However, their task and resulting dialogues lackthe typical complexity of conversations or teamwork. Further-more, the interpersonal synergy model was not clearly differ-entiated from other coordination-focused models of groundingwith explicit foundations in strategy and intentionality (i.e., au-dience design, joint activity, perspective taking). Here we testrecurrence-based models in a collaborative task that stressedthe grounding process. Results support a coordination modelof dialogue over the alignment model as a predictor of perfor-mance. Content-based mediation analyses showed that the co-ordination recurrence model includes critical aspects of strate-gic design and is not purely interpersonal synergy.