The tradeoff hypothesis in the speech–gesture relationship claims that (a) when gesturing gets harder, speakers will rely relatively more on speech, and (b) when speaking gets harder, speakers will rely relatively more on gestures. We tested the second part of this hypothesis in an experimental collaborative referring paradigm where pairs of participants (directors and matchers) identified targets to each other from an array visible to both of them. We manipulated two factors known to affect the difficulty of speaking to assess their effects on the gesture rate per 100 words. The first factor, codability, is the ease with which targets can be described. The second factor, repetition, is whether the targets are old or new (having been already described once or twice). We also manipulated a third factor, mutual visibility, because it is known to affect the rate and type of gesture produced. None of the manipulations systematically affected the gesture rate. Our data are thus mostly inconsistent with the tradeoff hypothesis. However, the gesture rate was sensitive to concurrent features of referring expressions, suggesting that gesture parallels aspects of speech. We argue that the redundancy between speech and gesture is communicatively motivated.