To probe internal motions in proteins on the 10(-8)-10(-5) s time scale by NMR relaxation, it is necessary to eliminate protein tumbling. Here, we examine to what extent magnetic relaxation dispersion (MRD) experiments on the water H-1 resonance report on protein motions in this time window, We also perform a critical test of two physically distinct mechanisms that have been proposed to explain and interpret H-1 MRD profiles from immobilized proteins: the exchange-mediated orientational randomization (EMOR) mechanism and the two-phase spin-fracton (2PSF) mechanism. For these purposes, we report the H-1 MRD profiles from protonated and partially deuterated ubiquitin, cross-Linked by glutaraldehyde. The EMOR approach, with the crystal structure of ubiquitin as input, accounts quantitatively for the MRD data and shows that hydroxyl-bearing side chains undergo large-amplitude motions on the microsecond time scale, In contrast, the 2PSF model, which attributes H-1 relaxation to small-amplitude backbone vibrations that propagate in a low-dimensional fractal space, fails qualitatively in describing the effect of H -> D substitution. These findings appear to resolve the tong-standing controversy over the molecular basis of water-H-1 relaxation in systems containing rotationally immobilized macromolecules, including biological tissue.