“Censorship resistant” systems attempt to prevent censors from imposing a particular distribution of content across a system. In this paper, we introduce a variation of censorship resistance (CR) that is resistant to selective filtering even by a censor who is able to inspect (but not alter) the internal contents and computations of each data server, excluding only the server’s private signature key. This models a service provided by operators who do not hide their identities from censors. Even with such a strong adversarial model, our definition states that CR is only achieved if the censor must disable the entire system to filter selected content. We show that existing censorship resistant systems fail to meet this definition; that Private Information Retrieval (PIR) is necessary, though not sufficient, to achieve our definition of CR; and that CR is achieved through a modification of PIR for which known implementations exist.