We have investigated the lattice relaxation around impurity atoms at the anion sublattice in CdTe, such as As acting as acceptor and Se which is isovalent to Te, with fluorescence detected EXAFS. We experimentally verify the lattice relaxation with a bond length being reduced by 8% around the As atom as inferred indirectly from ab-initio calculations of the electric field gradient in comparison with the measured value in a PAC experiment (S. Lany et al., Phys. Rev. B 62, R2259 (2000)). In the case of the isovalent impurity atom Se, the bond length is similarly reduced as determined experimentally by EXAFS and by model calculations with the density functional theory implemented in the WIEN97 program. In contrast to this inward relaxation, preliminary calculations for Br in CdTe, the next element in the series As, Se, and Br, which acts as donor at the Te sublattice, indicate an increase in bond length, an interesting prediction waiting for experimental verification.