When is a cellular-countably-compact space, countably compact?

We continue the study of cellular-compact spaces and the larger class of cellular-countably-compact spaces. We give a number of sufficient conditions involving local bases and local π -bases in order that a cellular-countably-compact space be countably compact and some conditions which imply that a topology is maximal with respect to being cellular-countably-compact are obtained. We also consider the compact productivity of the previously mentioned properties and give a characterization of those spaces whose product with a compact space is almost cellular-countably-compact.