A comprehensive study of high-K three-quasiparticle rotational bands in odd-A nuclei indicates the similarity in $\gamma$ -ray energies and dynamic moment of inertia $\Im^{(2)}$ . The extent of the identicality between the rotational bands is evaluated by using the energy factor method. For nuclei pairs exhibiting identical bands, the average relative change in the dynamic moment of inertia $\Im^{(2)}$ is also determined. The identical behaviour shown by these bands is attributed to the interplay of nuclear structure parameters: deformation and the pairing correlations. Also, experimental trend of the $ I(\hbar)$ vs. $\hbar \omega$ (MeV) plot for these nuclei pairs is shown to be in agreement with Tilted-Axis Cranking (TAC) model calculations.