The surface impurity ground states of anisotropic semiconductors are studied by two different methods, namely the perturbative variational method and the principle of minimal sensitivity which were developed recently. The treatment is based on (i) a parabolic one-band model and (ii) an infinite-barrier model for electronic states. In spite of the simplicity of the methods, it is found that the calculated energies for Ge and Si are very close to the results obtained by the conventional variational method. The validity of the variational trial wavefunction used in previous calculations is also discussed. A new variational trial function is also proposed for the case of the anisotropic crystals.