Our EXAFS results for the narrow-gap semiconductor alloy Hg1-xCdxTe show that the Hg-Te and Cd-Te bond lengths remain constant within 0.008Å between x = 0.15 and 1.0. Similarly, our investigation of bond lengths in the diluted magnetic semiconductors (DMS) Zn1-xMnxSe and Hg1-xMnxTe shows them to be essentially constant with x. We relate these results to previously published and currently developed theories.