We have defined a group of new parameterizations for P-wave in acoustic orthorhombic (ORT) media with three cross-term normal moveout velocities and three cross-term anellipticity parameters. The corresponding perturbation-based approximations for traveltime in ORT model are developed using the new parameterizations. The perturbation coefficients are computed by solving the eikonal equation in corresponding parameterization. Eight types of parameterization are defined based on the different elliptical background model and selection of anellipticity parameters. As the traveltime can be converted from the group velocity inverse, the sensitivity of the group velocity inverse to anellipticity parameters is analyzed for different parameterizations and different range of offsets. To stabilize the perturbation series and improve the accuracy, the Shanks transform is applied. From the comparison of traveltime after the Shanks transform using different parameterizations, we have concluded that the parameterization with vertical, two horizontal velocities, and three cross-term anellipticity parameters results in the best accuracy of traveltime function for P-wave in acoustic ORT medium.