Protection of privacy in databases has become of increasing importance. While a number of techniques have been proposed to query databases while preserving privacy of individual records in the database, very little is done to define a measure on how much privacy is lost after statistical releases. We suggest a definition based on information theory. Intuitively, the privacy loss is proportional to how much the descriptional complexity of a record decreases relative to the statistical release. There are some problems with this basic definition and we suggest ways to address these problems.