Speakers often communicate imprecisely, using expressions that are strictly speaking false yet felicitous. The degree to which imprecision is tolerated in discourse is governed by the Standard of Precision (SoP). While it is known that contextual factors can modulate the SoP, less is known about the discourse dynamics of imprecision. Previous accounts have claimed that implicit negotiations of the SoP are unidirectional: they only work upward, not downward. Here, we investigated whether parallel asymmetries arise when comprehenders adapt their SoPs in response to an interlocutor’s precision preferences. Results show bidirectional SoP adaptation effects: exposure to lower standards increased tolerance for imprecision, while exposure to higher standards reinforced stricter thresholds. These updates persisted beyond the dialogue, suggesting that exposure to (im)precise speakers modulates not only interpretations within a discourse, but also beyond the conversation. More broadly, our study provides a novel framework for studying real-time dynamic meaning negotiations during conversation.