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New structural results of the epitaxial growth of Co/Cu(111) in the coverage regime 1.5-15 ML are presented as investigated by quantitative LEED and STM. In the low coverage regime there is pure fcc stacking with copper diffused on top of 30% of the domains. The growth is ideally pseudomorphic. At intermediate coverages hcp stacked domains develop on the cost of fcc domains whereby the latter seem to be stabilized by their top copper layer. At high coverages the film is predominantly hcp exhibiting the ideal lattice parameter of Co(0001).