Summary: The authors give a revised form of the second part of Theorem 14 of their paper in the same journal 30, 189-211 (1983; Zbl 0524.54028): Let X be a completely regular space. If A can be expressed in the form \(G\cap S\), with G a paracompact set that is a \({\mathcal G}_{\delta}\)-set in \(\beta\) X, and with \(S\cap G\) a disjoint extended Souslin-\({\mathcal F}\) set in G, then A is a K-Lusin set in X. On the other hand, if A is a K-Lusin set in X, then A can be expressed in the form \(G\cap S\), with G a \({\mathcal G}_{\sigma}\)-set in \(\beta\) X, with S a Souslin-\({\mathcal F}\) set in \(\beta\) X, and with \(S\cap G\) a disjoint extended Souslin-\({\mathcal F}\) set in G.