Methods, apparatus, and systems for performing fault diagnosis are disclosed herein. In certain disclosed embodiments, methods for diagnosing faults from compressed test responses are provided. For example, in one exemplary embodiment, a circuit description of an at least partially scan-based circuit-under-test and a compactor for compacting test responses captured in the circuit-under-test is received. A transformation function performed by the compactor to the test responses captured in the circuit-under-test is determined. A diagnostic procedure for evaluating uncompressed test responses is modified into a modified diagnostic procedure that incorporates the transformation function therein. Computer-readable media comprising computer-executable instructions for causing a computer to perform any of the disclosed methods are also provided. Likewise, computer-readable media comprising lists of fault candidates identified by any of the disclosed methods or circuit descriptions created or modified by the disclosed methods are provided.