The structure of the electrochemically deposited Pb monolayer on Cu(lll) in 0.1M HClO4 was studied using in situ surface x-ray diffraction. The Pb monolayer forms an unrotated incommensurate hexagonal structure. The nearest-neighbor spacing of the Pb monolayer compresses continuously from 1.4% to 3.2%, of the bulk spacing as the electrode potential is varied, with no apparent tendency to lock in. The measured isothermal two-dimensional (2D) compressibility of the Pb monolayer, 0.95+/-0.07 Angstrom(2)/eV, is in good agreement with the value expected from the 2D free-electron gas model. The surface normal structure of the ph monolayer on Cu(111) was studied using reflectivity measurements. Fitting analysis based on a layered model revealed a contracted Pb-Cu spacing and an expanded topmost Cu layer. Unlike the in-plane structure, the surface norm al structure showed little potential dependence.