Nuclear magnetic relaxation dispersion (NMRD) measurements can provide valuable information about the dynamics and structure of macromolecular solutions and other complex fluids. A large number of 1 H NMRD studies of water in concentrated protein solutions and in semisolid biological samples have been reported. The observed dispersion usually extends over a wide frequency range and then cannot be described by a Lorentzian spectral density function. We propose here a model-free approach for analyzing such stretched dispersion profiles. Unlike the traditional empirical fitting procedures, the model-free approach is based on rigorous theory and produces parameters with well-defined physical significance. The model-free approach is validated with the aid of synthetic relaxation data, showing that it is robust and accurate, and is then applied to new water 1 H NMRD data from solutions of the protein bovine pancreatic trypsin inhibitor (BPTI). By separating the static and dynamic information content of the relaxation dispersion, the model-free analysis shows that the dramatic salt effect observed in BPTI solutions is due almost entirely to a slowing down of protein rotation with little change of protein structure. An analysis of the same data in terms of the empirical dispersion function used in most 1 H NMRD studies leads to a qualitatively different picture. We demonstrate that this widely used dispersion function is unphysical and that its parameters do not have the physical meaning usually ascribed to them.