Web personalization uses what systems know about us to create content targeted at our interests. When unwanted personalization suggests we are interested in sensitive or embarrassing topics, a natural reaction is to deny interest. This is a practical response only if denial of our interest is credible or plausible. Adopting a definition of plausible deniability in the usual sense of 'on the balance of probabilities,' we develop a practical and scalable tool called PDE, allowing a user to decide when their ability to plausibly deny interest in sensitive topics is compromised. We show that threats to plausible deniability are readily detectable for all the topics tested in an extensive testing program. Of particular concern is observation of threats to deniability of interest in topics related to health and sexual preferences. We show that this remains the case when attempting to disrupt search engine learning through noise query injection and click obfuscation. We design a defense technique exploiting uninteresting, proxy topics and show that it provides a more effective defense of plausible deniability in our experiments.