Deep research agents increasingly combine private local documents with external tools like web retrieval, creating a privacy risk: an agent's external queries may leak sensitive information. MosaicLeaks proposes a new deep-research task with multi-hop questions that interleave public and private information. Across the models we tested, agents frequently leaked private information, and training only for task performance made it worse. We propose a mosaic-leakage-aware RL training method, Privacy-Aware Deep Research (PA-DR) , which raises strict chain success (the share of chains where every hop is answered correctly) from 48.7% to 58.7% while reducing answer/full-information leakage from 34.0% to 9.9%. Privacy Leakage in Deep-Research Agents A research agent at a healthcare firm is working through a routine question, and along the way it fires off a handful of ordinary-looking web searches. …