Language models are deployed in settings that require compartmentalization: system prompts should not be disclosed, chain-of-thought reasoning is hidden from users, and sensitive data passes through shared contexts. We test whether models can keep prompted information out of their writing. We give each model a secret word with instructions not to reveal it, then ask it to write a story. A second model tries to identify the secret from the story in a binary discrimination test. The secret word never appears literally in any output, but all five frontier models we test leak it thematically -- through topic choice, imagery, and setting--6hy-at rates significantly different from chance, up to 79\%. When told to actively hide the secret, models write \emph{away from} it, and this avoidance is itself detectable. The leakage is cross-model readable, scales sharply with model size within two model families, and disappears entirely for short-form writing like jokes. Giving the model a decoy concept to ``focus on instead'' partially redirects the leakage from the real secret to the decoy. Attending to a secret appears to open up an information channel that frontier LLMs cannot close, even when instructed to.