Thermal conductivity measurements have been made from 50 mK to 100 K of Ni-doped GaAs samples containing different proportions of Ni+, Ni2+ and Ni3+. Resonant phonon scattering at 300 GHz is assigned to Ni2+ (3T1) and this is supported by studies of photoinduced changes in the Ni2+ concentration. The scattering is attributed to tunnelling within the ground state of an orthorhombic Jahn-Teller system. Uniaxial stress measurements show that the levels are very sensitive to both E and T2 strains and provide values of VEb and VTb. Data for Cr3+(4T1) in GaAs, GaP and InP are re-examined in the light of these results. It is proposed that the rich spectrum of resonance frequencies is due to multiple-ion effects caused by ion-ion coupling via the strain field.