Conversational partners align the meanings of their words over the course of interaction to coordinate and communicate. One process of alignment is lexical entrainment, whereby partners mirror and abbreviate their word usage to converge on shared terms for referents relevant to the conversation. However, lexical entrainment may result in inefficient mimicry that does not add new information, suggesting that task-oriented communication may favor alignment through other means. The present study investigates the process of alignment in Danish conversations in which dyads learned to categorize unfamiliar "aliens" using trial-and-error feedback. Performance improved as dyad communication became less verbose, measured as a decrease in the entropy of word usage. Word usage also diverged between partners as measured by Jensen-Shannon Divergence, which indicates that alignment was not achieved through lexical entrainment. A computational model of dyadic communication is shown to account for the alien game results in terms of joint least effort. The model shows that alignment of partner referents can increase as a result of minimizing both the joint entropy of dyadic word usage and the conditional entropy of individual referents given the joint signal distribution. We conclude that the principle of least effort, originally proposed to shape language evolution, may also support alignment in task-oriented communication.