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For immobilized protein the water proton T ₁-NMRD profile displays three enhanced relaxation peaks (QP). For slow tumbling proteins these relaxation peaks are not experimentally observed. However, the theoretically determined QP effect on the amide proton T ₁-NMRD profile displays a distorted Lorentzian dispersion profile. The question arises as to whether there is also a distortion of the water-proton T ₁-NMRD profile due to QP. The model of Sunde and Halle [J. Magn. Reson. 203, 257 (2010)] predicts a decreasing QP relaxation contribution and, with the aid of a model for tumbling proteins [P.-O. Westlund, Phys. Chem. Chem. Phys, 12, 3136 (2010)], it is shown that the QP effect is absent in water-proton T ₁-NMRD profiles for slow tumbling proteins with τ_R < 1 µs, τ_I.