Large Language Models (LLMs)  generate longform text by successively sampling the next token based on the probability distribution of the token vocabulary at each decoding step. Current popular truncation sampling methods such as top-sampling, also known as nucleus sampling, often struggle to balance coherence and creativity in generating text, particularly when using higher temperatures. To address this issue, we propose min-, a dynamic truncation sampling method, that establishes a minimum base percentage threshold for tokens, which the scales according to the probability of the top candidate token. Through experiments on several benchmarks, such as GPQA, GSM8K and AlpacaEval Creative Writing, we demonstrate that min-improves the coherence and quality of generated text even at high temperatures, while also facilitating more creative and diverse outputs compared to top-and other sampling methods. As of writing, min-has been adopted by multiple open-source LLM implementations, and have been independently assessed by members of the open-source LLM community, further validating its practical utility and potential111Code, evaluation code and results available athttps://github.com/menhguin/minp_paper/.