In a recent paper Kovács [1] studied join-continuous modular lattices which satisfy the following conditions: (i) every element is a join of finitely many join-irredicibles, and, (ii) the set of join-irreducibles satisfies the descending chain condition. He was able to prove that such a lattice must itself satisfy the descending chain condition. Interest was expressed in whether or not one could obtain the same result without the assumption of modularity and/or of join-continuity. In this paper we give an elementary proof of this result without the assumption of join- continuity (which of course must then follow as a consequence of the descending chain condition). In addition we give a suitable example to show that modularity may not be omitted in general.