Suppose that Alice, owner of a k-anonymous database, needs to determine whether her database, when adjoined with a tuple owned by Bob, is still k-anonymous. Suppose moreover that access to the database is strictly controlled, because for example data are used for experiments that need to be maintained confidential. Clearly, allowing Alice to directly read the contents of the tuple breaks the privacy of Bob; on the other hand, the confidentiality of the database managed by Alice is violated once Bob has access to the contents of the database. Thus the problem is to check whether the database adjoined with the tuple is still k-anonymous, without letting Alice and Bob know the contents of, respectively, the tuple and the database. In this paper, we propose two protocols solving this problem.