Deuteron nuclear magnetic resonance spin-lattice relaxation times T-1 have been measured for solitary water molecules (D2O) at low concentrations in apolar and polar organic solvents at 30 degrees C at high pressures; D2O (30 mM) in C6H6 UP to 90 MPa, D2O (60 mM) in CHCl3 up to 300 MPa, D2O (100 mM) in CH3CN up to 300 MPa. The rotational correlation times tau(2R) for D2O in the organic solvents increase with increasing pressure. The pressure effect on tau(2R) for D2O in Solution is considerably larger than that on tau(2R) and eta (viscosity) for the neat solvent. We have tested the two forms of modified Stokes-Einstein-Debye law; the linear and nonlinear forms are tau(2R) = tau(2R)(0) + S(eta/T) and tau(2R) = B(eta/T)(alpha), respectively. The rotational correlation times are linearly related to solvent viscosity divided by temperature (eta/T) with a large positive intercept (tau(2R)(0)>0) It is shown that the linear form is practically better, and that the nonlinear form constrained at eta/T=0 is invalid. The temperature-variable slope (S-T) and the pressure-variable one (S-p) are markedly different, the ratios of S-p to S-T being 0.2-0.3. The extended-diffusion models based on isolated binary collisions cannot be used to explain the observed pressure effect because of the neglect of the attractive solute-solvent interactions.