In this paper we extend our notion of projectable spinors ([9], Ch.1) to the framework of Spinc manifolds and deduce the basic formulas relating spinors on the base and the total space of Riemannian submersions with totally geodesic one-dimensional fibres. Some geometric applications concerning positive Kahler–Einstein complex contact manifolds (e.g. their characterisation as twistor spaces over positive quaternionic Kahler manifolds) are also given.