This paper describes an efficient NMR strategy for assigning the backbone resonances of an intrinsically unstructured protein (IUP), p21-KID, bound to its biological target, Cdk2/cyclin A. In order to overcome the challenges associated with the high molecular weight (75 kDa) and low solubility of the ternary complex (0.2 mM), we used perdeuteration, TROSY, and high-sensitivity cryogenic NMR probes at high magnetic-field strengths (i.e. 16.4, 18.8 and 21.1 Tesla). p21-KID was also prepared by using specific amino acid isotope labels. Most importantly, we studied binary, subcomplexes that allowed resonance assignments to be made in stages. We show that subdomains of p21-KID folded within binary complexes into the same conformations as observed in the ternary, Cdk2/cyclin A complex. This is a general feature of IUPs, which often adopt highly extended conformations when bound to other proteins. This strategy is suitable for studies of IUPs within considerably larger biomolecular assemblies as long as the IUP can be uniformly and selectively isotope labeled.