Abstract We study the dependence of energy spectra of odd- A nuclei on the signature in the framework of a quasiparticle-triaxial rotor model with various combinations of parameter values, expecting that the observed signature inversion in some odd- A nuclei may be explained as a consequence of a rotation around the shortest axis. If the irrotational flow (IRE) model is used for the moments of inertia, the obtained wave functions bear some similarity to rotation around the shortest axis only at low spins and the signature dependence is only slightly inverted. If the sign of γ of the IRF moments of inertia is reversed (γ-rev. IRE), one sees some characteristic features of rotation around the shortest axis in the resulting wave functions except at low spins and the signature dependence gets inverted depending on the condition. However, this occurs only for rather large values of γ.