CCR4-NOT is a conserved multiprotein complex which regulates eukaryotic gene expression principally via shortening of poly(A) tails of messenger RNA or deadenylation. Here, we reconstitute a complete, recombinant human CCR4-NOT complex. Our reconstitution strategy permits strict compositional control to test mechanistic hypotheses with purified component variants. CCR4-NOT is more active and selective for poly(A) than the isolated exonucleases, CCR4a and CAF1, which have distinct deadenylation profiles in vitro. The exonucleases require at least two out of three conserved non-enzymatic modules (CAF40, NOT10:NOT11 or NOT) for full activity in CCR4-NOT. CAF40 and the NOT10:NOT11 module both bind RNA directly and stimulate deadenylation in a partially redundant manner. Linear motifs from different RNA-binding factors that recruit CCR4-NOT to specific mRNAs via protein-protein interactions with CAF40 can inhibit bulk deadenylation. We reveal an additional layer of regulatory complexity to the human deadenylation machinery, which may prime it either for general or target-specific degradation.