The defect structures and spin Hamiltonian parameters (SHPs) for three Rh2+ centres (denoted C1 in KTiOAsO4 and C2 and C3 in KTiOPO4) are theoretically investigated by utilising the perturbation formulae for a 4d7 ion under orthorhombically (D2h) elongated octahedra. The defect structures are characterized by the axial elongation ratios of 4.91%, 4.93% and 4.90% along the Z axis and the planar bond length variation ratios of 0.05%, 0.01% and 0.04% for centres C1, C2 and C3, respectively, owing to the Jahn–Teller effect. The nearly identical moderate axial elongation ratios and the slightly different tiny planar bond length variation ratios may suitably account for the comparable moderate axial g anisotropies ∆g (≈0.6087, 0.6124 and 0.6067) and the slightly dissimilar tiny perpendicular g anisotropies δg (≈0.0649, 0.0097 and 0.0509) of the three centres, respectively. All centres demonstrate similar strong crystal-field interactions and moderate covalence arising from the comparable short impurity-ligand distances.