Confidentiality and integrity are often treated as dual properties in formal models of information-flow control, access control and many other areas in computer security. However, in contrast to confidentiality policies, integrity policies are less formally studied in the information-flow control literature. One important reason is that traditional noninterference-based information-flow control approaches give very weak integrity guarantees for untrusted code. Integrity and confidentiality policies are also different with respect to implicit information channels. This paper studies integrity downgrading policies in information-flow control and compares them with their confidentiality counterparts. We examine the drawbacks of integrity policies based on noninterference formalizations and study the integrity policies in the framework of downgrading policies and program equivalences. We give semantic interpretations for traditional security levels for integrity, namely, tainted and untainted, and explain the interesting relations between confidentiality and integrity in this framework.