Wafer-scale growth of metallic films into single crystals is challenging owing to the large lattice mismatch and uncontrollable stacking of atoms during deposition. Here, single-crystal Ag(111) films are grown on flat Cu(111) buffer layers using atomic sputtering epitaxy, notwithstanding the large (approximately 13%) Ag/Cu lattice mismatch. Phenomenologically, the mismatch strain is localised to the first Ag monoatomic interface layer, without spreading into adjacent Ag layers. This perfect strain absorber occurs owing to regulated in-plane displacements of Ag atoms at the periodic colocalisation loci of Ag and Cu atoms. This extreme case does not require collective cooperation of dislocated atoms as opposed to the case of strain relaxation, thereby enabling defect-free growth of Ag films. The resulting film surfaces are inherently ultraflat and thus advantageous for perfect reflectors and plasmonic devices.