Recognition of RNA by proteins and small molecules often involves large changes in RNA structure and dynamics, yet very few studies have so far characterized these motional changes. Here we extend to the protein-bound RNA recent 13C relaxation studies of motions in the RNA recognized by human U1A protein, a well-known model for protein-RNA recognition. Changes in relaxation observed upon complex formation demonstrate that the protein-binding site becomes rigid in the complex, but the upper stem-loop that defines the secondary structure of this RNA experiences unexpected motional freedom. By using a helix elongation strategy, we observe that the upper stem-loop moves independently of the remainder of the structure also in the absence of U1A. Surprisingly, RNA residues making important intermolecular contacts in the structure of the complex exhibit increased flexibility in the presence of the protein. Both of these results support the hypothesis that RNA-binding proteins select a structure that optimizes intermolecular contacts in the manifold of conformations sampled by the free RNA and that protein binding quenches these motions. Together with previous studies of the RNA-bound protein, they also demonstrate that protein-RNA interfaces experience complex motions that modulate the strength of individual interactions.