This paper advocates a modified parameterization for transversely isotropic (TI) media in seismology. Transversely isotropic media may be parameterized by the reference quasi-compressional (qP) and quasi-shear (qSV) velocities, α and β, together with the two parameters, ε and δ. These last two variables account for the deviation of the coupled qP and qSV modes of wave propagation from the isotropic case. The dimensionless quantity ε is a measure of the ellipticity of the qP wavefront. The “strange” parameter δ has been employed as a measure of deviation of the qP wavefront or slowness surface from an ellipsoid of revolution and also of the qSV wavefront or slowness surface from a sphere. As the parameter δ has been described as “conceptually inaccessible”; it is logical to determine an alternative characterization in physically realizable quantities. As in the earlier literature, the defining parameter for the degree of ellipticity of the qP slowness or energy surface in a TI medium is chosen here to be ε. In addition, the deviation of both the qP and qSV surfaces from the degenerate ellipsoidal case will be specified here as σ. An examination of the linearized phase (wavefront normal) velocities, and the linearized PP and SVSV reflection coefficients at an interface between two TI media is undertaken to emphasize the merits of this modified parameterization. All formulae used here have appeared in one form or another in the cited literature. In this paper, a reformulation of existing equations as functions of the two independent variables, (ε, σ), is presented. This results in a more physically realizable context for the linearized formulae.