This work is concerned with the question of calculating transition oscillator strengths for atomic fine-structure levels that are described by strongly mixed superpositions of terms. Rather accurate non-relativistic calculations of wavefunctions followed by perturbation treatment of relativistic interactions can lead to very poor term mixing, hence poor oscillator strengths, in situations where there is near degeneracy of the non-relativistic energy eigenvalues. It is shown in a three-term mixing case how a corrected Hamiltonian can be constructed using observed level energies as known input. The example, involving the three J=2 levels of the 2p⁵3p configuration of neutral neon, shows a dramatic improvement for transition probabilities and Lande factors when the correction is made and the results compared with recent observations.