Privacy preserving analytics on statistical databases is an old problem. Analysts want to query high quality statistical information across the user population of a database. At the same time, obtaining isolated information about a single user needs to be prevented. User privacy can be successfully protected by a number of techniques, such as adding noise to the content or results of a database or limiting the number of possible queries. Unfortunately, all of them reduce the quality of statistics and usability to a point that none has been widely adopted by industry. In this report we explore the extent to which one can lift the limitations on statistical quality without giving up much in terms of privacy protection. We present ANON, a new point in the design space that—contrary to many previous techniques—also takes queries into account. Through limiting and active monitoring of queries and results, ANON is able to reduce the amount of noise needed and increase the number of queries allowed. We describe and analyse the design of ANON as well as our findings from experimental attacks on real-world data.