We consider a spin-1/2 impurity interacting with conduction electrons in two different orbital channels via an isotropic spin exchange. The exchange is the same for both channels, but a crystalline field breaks the symmetry between the orbital channels. This corresponds to a splitting of the conduction electron Γ8 into two doublets in the quadrupolar Kondo effect and to the application of an external magnetic field in the electron assisted tunneling of an atom in a double-well potential. We study the ground-state properties of the impurity as a function of the magnetic and crystalline fields. The crystalline field quenches the critical behavior of the overcompensated fixed point: The impurity ground state is a singlet.