A drive towards efficiency seems to regulate communicative processes and ultimately language change. In line with efficiency principles, signed, spoken, and/or gestural utterances tend to reduce in overall effort over repeated referrals in referential tasks. Such reduction is often studied in individuals, using a single communicative modality. Here we seek to understand reduction of communicative effort in its natural communicative environment, i.e. during multimodal and collaborative face-to-face dialogues about displaced referents. We ascertain that the reduction in joint effort over repeated referrals actually follows a negative power relationship. This reduction in communicative effort is multimodal, occurring across gesture, speech, prosody, and turn taking, and it is interactive, based on joint effort. The effect is robust, being confirmed through a reanalysis of published datasets about (individual) effort reduction. Crucially, the effect is also communicatively relevant. The coefficient of the power relationship predicts change and convergence in interlocutors’ conceptualizations of the communicative referents. Assuming that the coefficient of the negative power relationship reflects how well effort translates into mutual understanding - a process we call communicative work - we suggest that the power function captures a complementary strategy of increasing initial exploration and applying efficient selection for an effective joint conceptualization of referents. The current report invites linguistic theory, agent-based modeling, and experimental psychological inquiries into understanding the general principles of what could amount to a ‘power law of joint communicative work’.