We show that nuclear <i>C</i><sup>*</sup>-algebras have a refined version of the completely
positive approximation property, in which the maps that approximately factorize
through finite dimensional algebras are convex combinations of order zero maps.
We use this to show that a separable nuclear <i>C</i><sup>*</sup>-algebra A which is closely
contained in a <i>C</i><sup>*</sup>-algebra B embeds into B