By dephosphorylating the C-terminal domain (CTD) of RNA polyrnerase II (Pot H), the Transcription Factor IIF (TFIIF)-associating CTD phosphatase (FCP1) performs an essential function in recycling Pol II for subsequent rounds of transcription. The interaction between FCP1 and TFIIF is mediated by the disordered C-terminal tail of FCP1, which folds to form an a-helix upon binding the RAP74 subunit of TFIIF. The present work reports a structure-based simulation study of this interaction between the folded winged-helix domain of RAP74 and the disordered C-terminal tail of FCP1. The comparison of measured and simulated chemical shifts suggests that the FCP1 peptide samples 40-60% of its native helical structure in the unbound disordered ensemble. Free energy calculations suggest that productive binding begins when RAP74 makes hydrophobic contacts with the C-terminal region of the FCP1 peptide. The FCP1 peptide then folds into an amphipathic helix by zipping up the binding interface. The relative plasticity of FCP1 results in a more cooperative binding mechanism, allows for a greater diversity of pathways leading to the bound complex, and may also eliminate the need for "backtracking" from contacts that form out of sequence.