In Saccharomyces cerevisiae, non-coding RNAs, including cryptic unstable transcripts (CUTs), are subject to degradation by the exosome. The Trf4/5-Air1/2-Mtr4 polyadenylation (TRAMP) complex in S. cerevisiae is a nuclear exosome cofactor that recruits the exosome to degrade RNAs. Trf4/5 are poly(A) polymerases, Mtr4 is an RNA helicase, and Air1/2 are putative RNA-binding proteins that contain five CCHC zinc knuckles (ZnKs). One central question is how the TRAMP complex, especially the Air1/2 protein, recognizes its RNA substrates. To characterize the function of the Air1/2 protein, we used random mutagenesis of the AIR1/2 gene to identify residues critical for Air protein function. We identified air1-C178R and air2-C167R alleles encoding air1/2 mutant proteins with a substitution in the second cysteine of ZnK5. Mutagenesis of the second cysteine in AIR1/2 ZnK1-5 reveals that Air1/2 ZnK4 and -5 are critical for Air protein function in vivo. In addition, we find that the level of CUT, NEL025c, in air1 ZnK1-5 mutants is stabilized, particularly in air1 ZnK4, suggesting a role for Air1 ZnK4 in the degradation of CUTs. We also find that Air1/2 ZnK4 and -5 are critical for Trf4 interaction and that the Air1-Trf4 interaction and Air1 level are critical for TRAMP complex integrity. We identify a conserved IWRXY motif in the Air1 ZnK4-5 linker that is important for Trf4 interaction. We also find that hZCCHC7, a putative human orthologue of Air1 that contains the IWRXY motif, localizes to the nucleolus in human cells and interacts with both mammalian Trf4 orthologues, PAPD5 and PAPD7 (PAP-associated domain containing 5 and 7), suggesting that hZCCHC7 is the Air component of a human TRAMP complex.