The fluency and general applicability of large language models (LLMs) has motivated significant interest in detecting whether a piece of text was written by a language model. While both academic and commercial detectors have been deployed in some settings, particularly education, other research has highlighted the fragility of these systems. In this paper, we demonstrate a data-efficient attack that fine-tunes language models to confuse existing detectors, leveraging recent developments in reinforcement learning of language models. We use the 'human-ness' score (often just a log probability) of various open-source and commercial detectors as a reward function for reinforcement learning, subject to a KL-divergence constraint that the resulting model does not differ significantly from the original. For a 7B parameter Llama-2 model, fine-tuning for under a day reduces the AUROC of the OpenAI RoBERTa-Large detector from 0.84 to 0.62, while perplexity on OpenWebText increases from 8.7 to only 9.0; with a larger perplexity budget, we reduce AUROC to 0.30 (worse than random), with a perplexity increase to 9.9. Similar to traditional adversarial attacks, we find that this increase in `detector evasion' generalizes to other detectors not used during training. In light of our empirical results, we advise against continued reliance on LLM-generated text detectors.