Intrinsically unstructured proteins (IUPs) exist in a disordered conformational state, often considered to be equivalent with the random-coil structure. We challenge this simplifying view by limited proteolysis, circular dichroism (CD) spectroscopy, and solid-state (1)H NMR, to show short- and long-range structural organization in two IUPs, the first inhibitory domain of calpastatin (CSD1) and microtubule-associated protein 2c (MAP2c). Proteases of either narrow (trypsin, chymotrypsin, and plasmin) or broad (subtilisin and proteinase K) substrate specificity, applied at very low concentrations, preferentially cleaved both proteins in regions, i.e., subdomains A, B, and C in CSD1 and the proline-rich region (PRR) in MAP2c, that are destined to form contacts with their targets. For CSD1, nonadditivity of the CD spectra of its two halves and suboptimal hydration of the full-length protein measured by solid-state NMR demonstrate that long-range tertiary interactions provide the structural background of this structural feature. In MAP2c, such tertiary interactions are absent, which points to the importance of local structural constraints. In fact, urea and temperature dependence of the CD spectrum of its PRR reveals the presence of the extended and rather stiff polyproline II helix conformation that keeps the interaction site exposed. These data suggest that functionally significant residual structure exists in both of these IUPs. This structure, manifest as either transient local and/or global organization, ensures the spatial exposure of short contact segments on the surface. Pertinent data from other IUPs suggest that the presence of such recognition motifs may be a general feature of disordered proteins. To emphasize the possible importance of this structural trait, we propose that these motifs be called primary contact sites in IUPs.