A general method to enhance the sensitivity of the multidimensional NMR experiments performed at high-polarizing magnetic field via the significant reduction of the longitudinal proton relaxation times is described. The method is based on the use of two vast pools of "thermal bath" H-1 spins residing on hydrogens covalently attached to carbon and oxygen atoms in C-13,N-15 labeled and fully protonated or fractionally deuterated proteins to uniformly enhance longitudinal relaxation of the H-1(N) spins and concomitantly the sensitivity of multipulse NMR experiments. The proposed longitudinal relaxation optimization is implemented in the 2D [N-15,H-1]-LTROSY, 2D [N-15,H-1]-LHSQC and 3D LTROSY-HNCA experiments yielding the factor 2-2.5 increase of the maximal signal-to-noise ratio per unit time at 600 MHz. At 900 MHz, the predicted decrease of the (HN)-H-1 longitudinal relaxation times can be as large as one order of magnitude, making the proposed method an important tool for protein NMR at high magnetic fields.