In the process of collectively inventing new words for new concepts in a population, conflicts can quickly become numerous, in the form of synonymy and homonymy. Remembering all of them could cost too much memory, and remembering too few may slow down the overall process. Is there an efficient behavior that could help balance the two? The Naming Game is a multi-agent computational model for the emergence of language , focusing on the negotiation of new lexical conventions, where a common lexicon self-organizes but going through a phase of high complexity. Previous work has been done on the control of complexity growth in this particular model, by allowing agents to actively choose what they talk about. However , those strategies were relying on ad hoc heuristics highly dependent on fine-tuning of parameters. We define here a new principled measure and a new strategy, based on the beliefs of each agent on the global state of the population. The measure does not rely on heavy computation, and is cognitively plausible. The new strategy yields an efficient control of complexity growth, along with a faster agreement process. Also, we show that short-term memory is enough to build relevant beliefs about the global lexicon.