Previous work has shown that artificial neural agents naturally develop surprisingly non-efficient codes. This is illustrated by the fact that in a referential game involving a speaker and a listener neural networks optimizing accurate transmission over a discrete channel, the emergent messages fail to achieve an optimal length. Furthermore, frequent messages tend to be longer than infrequent ones, a pattern contrary to the Zipf Law of Abbreviation (ZLA) observed in all natural languages. Here, we show that near-optimal and ZLA-compatible messages can emerge, but only if both the speaker and the listener are modified. We hence introduce a new communication system, “LazImpa”, where the speaker is made increasingly lazy, i.e., avoids long messages, and the listener impatient, i.e., seeks to guess the intended content as soon as possible.