Using scanning tunneling microscopy experiments in combination with first-principles calculations we have studied the geometric structure of the compressed c(7sqrt(2) × sqrt(2)) antiphase domain structure of CO on Cu(001). We find direct evidence for structural relaxations involving an inhomogeneous CO environment characterized by molecular tilting, bending, and nonterminal sites. Our analysis solves the long-standing problem of the adsorption structure of the compressed phase and is important for understanding the physical properties of this fundamental adsorption system.