As participants repeatedly interact using graphical signals (as in a game of Pictionary), the signals gradually shift from being iconic (or motivated) to being symbolic (or arbitrary). The aim here is to test experimentally whether this change in the form of the signal implies a concomitant shift in the inferential mechanisms needed to understand it. The results show that, during early, iconic stages, there is more reliance on creative inferential processes associated with insight problem solving, and that the recruitment of these cognitive mechanisms decreases over time. The variation in inferential mechanism is not predicted by the sign's visual complexity or iconicity, but by its familiarity, and by the complexity of the relevant mental representations. The discussion explores implications for pragmatics, language evolution, and iconicity research.