Sometimes it happens that hamiltonian has degenerate eigenvalue. This degeneracy can be removed by modifying the Hamiltonian. If the modification is additional term proportional to an adjustable parameter, the resulting difference between the eigenvalues can be made arbitrarily small. Is there some phenomenon or experiment that requires the eigenvalues to be exactly degenerate, or is it possible to always use eigenvalues that are close enough but different with virtually the same result ? In other words, is degeneracy necessary for explanation of some experiments, or is it just an artefact maintained by the use of simple hamiltonians?