We present a novel framework, called Private Disclosure of Information (PDI), which is aimed to prevent an adversary from inferring certain sensitive information about subjects using the data that they disclosed during communication with an intended recipient. We show cases where it is possible to achieve perfect privacy regardless of the adversary's auxiliary knowledge while preserving full utility of the information to the intended recipient and provide sufficient conditions for such cases. We also demonstrate the applicability of PDI on a real-world data set that simulates a health tele-monitoring scenario.