This paper deals with a class of topological spaces in which α-compactness and compactness coincide and the tightness of a compact subset is less or equal than α, a being an infinite cardinal number. This class is a natural extension of the class of strictly angelic spaces, introduced by W . Govaerts . Sufficient conditions are given for a space of continuous functions to belong to this class, and some results on locally convex spaces are obtained as an application.