In this paper, we present a new subring of C(X) that contains the subring Cc(X), the set of all continuous functions with countable image. We observe that Lcc(X) enjoys most of the important properties which are shared by C(X) and Cc(X). It is shown that any hereditary lindelöf scattered space is functionally countable. Spaces X such that Lcc(X) is regular (von Neumann) are characterized and it is shown that ℵ0-selfinjectivity and regularity of Lcc(X) coincide.