In face-to-face communication, speakers typically integrate information acquired through different sources, including what they see and what they know, into their communicative messages. In this study, we asked how these different input sources influence the frequency and type of iconic gestures produced by speakers during a communication task, under two degrees of task complexity. Specifically, we investigated whether speakers gestured differently when they had to describe an object presented to them as an image or as a written word (input modality) and, additionally, when they were allowed to explicitly name the object or not (task complexity). Our results show that speakers produced more gestures when they attended to a picture. Further, speakers more often gesturally depicted shape information when attended to an image, and they demonstrated the function of an object more often when they attended to a word. However, when we increased the complexity of the task by forbidding speakers to name the target objects, these patterns disappeared, suggesting that speakers may have strategically adapted their use of iconic strategies to better meet the task’s goals. Our study also revealed (independent) effects of object manipulability on the type of gestures produced by speakers and, in general, it highlighted a predominance of molding and handling gestures. These gestures may reflect stronger motoric and haptic simulations, lending support to activation-based gesture production accounts.