Polite speech poses a fundamental alignment challenge for large language models (LLMs). Humans deploy a rich repertoire of linguistic strategies to balance informational and social goals – from positive approaches that build rapport (compliments, expressions of interest) to negative strategies that minimize imposition (hedging, indirectness).We investigate whether LLMs employ a similarly context-sensitive repertoire by comparing human and LLM responses to English-language scenarios in both constrained and open-ended production tasks.We find that larger models (≥70B parameters) successfully replicate key effects from the computational pragmatics literature, and human evaluators prefer LLM-generated responses in open-ended contexts. However, further linguistic analyses reveal that models disproportionately rely on negative politeness strategies to create distance even in positive contexts, potentially leading to misinterpretations. While LLMs thus demonstrate an impressive command of politeness strategies, these systematic differences provide important groundwork for making intentional choices about pragmatic behavior in human-AI communication.