Let X be a compactum possessing a binary normal subbase S for its closed subsets. Then every set-valued S-continuous map : Z → X with closed S-convex values, where Z is an arbitrary space, has a continuous single-valued selection. More gener-ally, if A ⊂ Z is closed and any map from A to X is continuously extendable to a map from Z to X, then every selection for |A can be extended to a selection for . This theorem implies that if X is a -metrizable (resp., -metrizable and connected) compactum with a normal binary closed subbase S, then every open S-convex surjection f : X → Y is a zero-soft (resp., soft) map. Our results provide some generalizations and specifications of Ivanov’s results (see [5–7]) concerning superextensions of-metrizable compacta