The NMR deuteron spin–lattice relaxation times T1, self-diffusion coefficients D, and shear viscosities η have been measured as a function of pressure in the temperature interval −15 to 10°C. The low-pressure extreme of the measurements is Ice I, whereas Ice V represents the high-pressure boundary of the experiments. In analogy with anomalous motional behavior in compressed liquid water, the initial compression of liquid D2O in the temperature interval studied results in higher motional freedom of D2O molecules so that T1 and D dependences with pressure exhibit a maximum and shear viscosity shows a minimum. This is a result of distortion and weakening of the hydrogen bond network owing to compression. Further compression hinders molecular motions as a result of increased repulsive interactions due to higher packing. This study also enables us to test the applicability of hydrodynamic equations at the molecular level for liquid heavy water. Analysis of the relaxation and shear viscosity data show that the Debye equation fails to describe the density effects on reorientation of D2O molecules. It appears that the success of the Debye equation to describe temperature effects on reorientation of H2O and D2O molecules at 1 bar is accidental. However, the data show that the deuteron relaxation rate (1/T1)D is proportional to η/T under isochoric conditions. The fact that the slope of the (1/T1)D vs η/T plot diminishes with increasing density indicates that compression leads to diminished coupling between rotational and translational motions of water molecules. The shear viscosity and self-diffusion data show that the Stokes–Einstein equation does not represent the relationship between D and η in liquid heavy water. A brief discussion of the isotope effects on shear viscosity in liquid D2O and H2O is presented.