We present a perturbative approach for the resonant tunnel splittings of an arbitrary effective single spin system. The Hamiltonian of such a system contains a uniaxial anisotropy, a transversal magnetic field and a second-order transversal anisotropy. Further, we investigate the influence of the transversal magnetic field on the energy splittings for higher integer quantum spins and we introduce an exact formula, which defines values of the transversal magnetic field, the transversal anisotropy and the uniaxial anisotropy where the contribution of the transversal magnetic field to the energy splitting is at least equal to the contribution of the transversal anisotropy.