We show the importance of considering the detailed local distributions of oxygen atoms around tellurium in CdTeO (x) glasses when interpreting X-ray photoemission experiments. We perform first principles calculations of core-level shifts that are used to compute X-ray photo-electron spectra. The core-level shifts are investigated by means of atomic density of states and a structural Voronoi analysis. We find that the dominating effect on the atomic core-level shift of tellurium is charge redistribution due to the oxygen atoms. There is however also a prominent effect from the geometrical arrangement of the oxygen neighbors.