To date the problem of finding a general characterization of injective enumerability of recursively enumerable (r.e) classes of r.e. sets has proved intractable. This paper investigates the problem for r.e. classes of cofinite sets. We state a suitable criterion for r.e. classesC such that there is a boundn∈ω with |ω-A|≤n for allA∈C. On the other hand an example is constructed which shows that Lachlan's condition (F) does not imply injective enumerability for r.e. classes of cofinite sets. We also look at (...) a certain embeddability property and show that it is equivalent with injective enumerability for certain classes of cofinite sets. At the end we present a reformulation of property (F). (shrink)