Abstract Higher excited states of acceptors in CdTe and ZnTe are obtained by using the Baldereschi and Lipari spherical model including the cubic correction and the central-cell effect. This is done by solving the coupled radial equations by the finite-element method with Arnoldi's algorithm, which gives several (≅20) low-lying states simultaneously. Our procedure allows one to determine very accurately the host band-structure parameters. In the case of CdTe we obtain the Luttinger parameters γ 1 = 5.30, γ 2 = 1.62, γ 3 = 2.10 and the dielectric constant ϵ 0 = 9.3. For ZnTe we obtain γ 1 = 3.80, γ 2 = 0.86, γ 3 = 1.32 and ϵ 0 = 9.4.