For every concerete category (A,U) over a complete base category X, Ch. Ehresmann has constructed a concrete completion. The objects of his completion are obtained by a transfinite process. J Adámek and V. Koubek have been able to obtain the objects of such a completion in one step, but still need a transfinite process to obtain the morphisms. In this paper a one-step-construction for such a completion is provided. The latter two completions are characterized by the obvious universal property, hence equivalent. The first completion is different.