In this paper, the relation between the notion of a discrete functor (see [4]) and the notion of a fine functor (see [1]) is examined. As a generalization of the notion of a F-fine object (see [1]), discrete functors T:A→Xare used to defineK-fine objects, whereKis a class ofA-objects. It is shown that if T is in addition semi-topological, then (as for F-fine objects in a topological category, see [1]) the class ofK-fine objects determines a bicoreflective subcategory ofA. Moreover, it is shown that in co-complete, co-(well-powered) categories, the existence of bicoreflective subcategories is equivalent to the existence of functors that are both discrete and semi-topological.