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A particle-rotor model with a nonspheroidal axial and reflection symmetric Woods-Saxon potential has been used to describe the rotational bands and gamma branching ratios in some odd-mass nuclei with 95 to 89 neutrons. Systematics of the deformation parameters have been found by calculations in the well-deformed region. The model is capable of giving a systematic classification of the low-lying odd-parity excitations in the N = 91 and expecially in the N = 89 nuclei. An important result is the identification of the 7/2+, 3/2+ and 5/2+ members of the 3/2+[651] side band in the weakly deformed nuclei. These discoveries also provide a reliable foundation for the classification of other low-spin states.