We have measured the lattice distortion around As (acceptor), Se (isovalent), and Br (donor) in CdTe with fluorescence detected X-ray absorption spectroscopy (XAFS). The experimental challenge lies in the compromise between a concentration high enough for X-ray absorption and low enough to avoid compensation and clustering. We could experimentally verify the lattice relaxation with a bond length reduction of 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 Perturbed Angular Correlation (PAC) experiment as recently reported. Our calculations of relaxation were performed with the WIEN97 package using the linearised augmented plane wave (LAPW) method and the FHI96md pseudopotential (PP) program. Using a super-cell approach for As on the Te site in CdTe, we find good convergence with increasing cell size so that the result can be taken as representative for the low doping limit. The extension to the neighbouring isovalent element Se again yields perfect agreement between experiment and model calculation with a sizeable lattice mismatch. In the case of Br, we find a sizeable increase of the bond length which may be taken as evidence for the high tendency of Br to form a Br A-center (Br plus metal vacancy) in CdTe. (c) 2004 Elsevier B.V. All rights reserved.