High-pressure angle-dispersive X-ray diffraction measurements show that Cd_0.80Hg_0.20 alloy remains in the hcp structure up to 50 GPa. We observe subtle anomalies in the pressure variation of the lattice parameters and their ratio, and in normalized stress versus strain. Electronic-structure calculations, as well as experimental and theoretical results for Cd, suggest that these anomalies are related to the occurrence of electronic topological transitions. Our results support Lifshitz’s prediction that electronic phase transitions can cause anomalies in structural and elastic properties of materials.