We have determined the structures of dense adlayers of glycine and alanine on the Cu(110) and Cu(100) surfaces using plane wave density functional theory. These calculations resolve several experimental controversies regarding these structures. Glycine exists on Cu(1 10) as a single adlayer structure, while on Cu(100) two distinct glycine adlayers coexist. The glycine structures serve as useful starting points for constructing alanine adlayer structures. We considered separately the adsorption of enantiopure alanine and racemic alanine on each surface. Adlayers of enantiopure alanine are found to be closely related to the adlayers observed for glycine. Racemic alanine adlayers on Cu(I 10) are structurally analogous to those observed for glycine on this surface and adopt a pseudo-racemate ordering. On Cu(100), in contrast to glycine, racemic alanine is found to adopt a single adlayer structure that is an ordered racemate. Spontaneous segregation of molecular enantiomers does not occur in racemic adsorbed mixtures on either surface. Consideration of the orientationally distinct domains that may exist for each adlayer on these surfaces provides important information for the interpretation of the adlayer domain boundaries that are commonly observed in scanning tunneling microscopy images of amino acid adlayers. Examining this set of amino acid adlayers provides useful insight into the range of subtle behaviors that can arise in these and related systems where chiral molecules form ordered adlayers on flat metal surfaces.