The measurement of residual dipolar couplings in weakly aligned proteins can potentially provide unique information on their structure and dynamics in the solution state. The challenge is to extract the information of interest from the measurements, which normally reflect a convolution of the structural and dynamic properties. We discuss here a formalism which allows a first order separation of their effects, and thus, a simultaneous extraction of structural and motional parameters from residual dipolar coupling data. We introduce some terminology, namely a generalized degree of order, which is necessary for a meaningful discussion of the effects of motion on residual dipolar coupling measurements. We also illustrate this new methodology using an extensive set of residual dipolar coupling measurements made on (15)N,(13)C-labeled human ubiquitin solvated in a dilute bicelle solution. Our results support a solution structure of ubiquitin which on average agrees well with the X-ray structure (Vijay-Kumar, et al., J. Mol. Biol. 1987, 194, 531--544) for the protein core. However, the data are also consistent with a dynamic model of ubiquitin, exhibiting variable amplitudes, and anisotropy, of internal motions. This work suggests the possibility of primary use of residual dipolar couplings in characterizing both structure and anisotropic internal motions of proteins in the solution state.