Thermal conductivity measurements have been made from 50 mK to 100 K of GaP and InP samples doped with Ni or V. The GaP samples both show strong resonant phonon scattering at 500 and 380 GHz respectively which is attributed to the T₁-T₂ tunnelling splitting associated with a dynamic orthorhombic Jahn-Teller distortion of the T₁ orbital ground state of Ni²⁺ and V²⁺. Low-frequency scattering in both systems is tentatively attributed to these same ions in complex with a defect. The assignment of the scattering to V²⁺ is supported by studies of photo-induced changes in the V²⁺ concentration. Uniaxial stress measurements on GaP:V suggest strong coupling to E modes but the strength of the coupling to T₂ modes is less clear. The absence of resonance scattering in a n-type sample of InP:Ni suggests the Ni is all in the Ni⁺ state (²T₂) as expected and the absence of scattering in n-type InP:V is consistent with the instability of V²⁺ in that system.