Text-based search queries reveal user intent to the search engine, compromising privacy. Topical Intent Obfuscation (TIO) is a promising new approach to preserving user privacy. TIO masks topical intent by mixing real user queries with dummy queries matching various different topics. Dummy queries are generated using a Dummy Query Generation Algorithm (DGA). We demonstrate various shortcomings in current TIO schemes, and show how to correct them. Current schemes assume that DGA details are unknown to the adversary. We argue that this is a flawed assumption, and show how DGA details can be used to construct efficient attacks on TIO schemes, using an iterative DGA as an example. Our extensive experiments on real data sets show that our attacks can flag up to 80% of dummy queries. We also propose HDGA, a new DGA that we prove to be immune to the attacks based on DGA semantics that we describe.