The angular distributions of the analysing power and the relative cross-sections for the elastic scattering of polarized He-3 nuclei by H-2 have been measured at incident He-3 energies of 22.5, 24, 27, 30 and 33 MeV. The data, considered in terms of fitted Legendre polynomials, clearly show a structure near 30 MeV He-3 energy which is more striking for odd L coefficients. In addition; our data, along with other data on the differential cross sections and on the analysing power for the scattering of polarized 2H, have been analysed for the phase shifts and mixing parameters in the S-matrix description. The phase shifts selected are compared with those from resonating-group theory calculations. The prominent residual differences were attributed to further resonances which involve the formation of Li-5 nuclei at high excitation energy. Finally a level scheme is compared with the predictions of a multi-particle, multi-shell model calculation. (C) 2000 Elsevier Science B.V. All rights reserved.