C(X) (resp. C *(X)) will denote as usual the ring of all (resp. all bounded) continuous functions into the real line R. Define C #(X) to consist of all f∊C(X) whose image M(f) in the residue class ring C(X)jM is real for every maximal ideal M in C(X). Then C # shares with C * the property of being an intrinsically determined subalgebra of C. Then C* shares with C* the property of being an intrinsically determined subalgebra of C. The compactification corresponding to C# (as uniformity determining subalgebra of C*) is thus also an intrinsically determined one. We show that this compactification is well known and "natural" in the cases of several elementary spaces X.