The Cyc8-Tup1 corepressor complex is targeted to promoters by pathway-specific DNA-binding repressors, thereby inhibiting the transcription of specific classes of genes. Genetic screens have identified mutations in a variety of Pol II holoenzyme components (Srb8, Srb9, Srb10, Srb11, Sin4, Rgr1, Rox3, and Hrs1) and in the N-terminal tails of histones H3 and H4 that weaken repression by Cyc8-Tup1. Here, we analyze the effect of individual and multiple mutations in many of these components on transcriptional repression of natural promoters that are regulated by Cyc8-Tup1. In all cases tested, individual mutations have a very modest effect on SUC2 RNA levels and no detectable effect on levels of ANB1, MFA2, and RNR2. Furthermore, multiple mutations within the Srb components, between Srbs and Sin4, and between Srbs and histone tails affect Cyc8-Tup1 repression to the same modest extent as the individual mutations. These results argue that the weak effects of the various mutations on repression by Cyc8-Tup1 are not due to redundancy among components of the Pol II machinery, and they argue against a simple redundancy between the holoenzyme and chromatin pathways. In addition, phenotypic analysis indicates that, although Srbs8-11 are indistinguishable with respect to Cyc8-Tup1 repression, the individual Srbs are functionally distinct in other respects. Genetic interactions among srb mutations imply that a balance between the activities of Srb8 + Srb10 and Srb11 is important for normal cell growth.