In this paper we introduce some pressure segregation methods obtained from a non-standard version of the discrete monolithic system, where the continuity equation has been replaced by a pressure Poisson equation obtained at the discrete level. In these methods it is the velocity instead of the pressure the extrapolated unknown. Moreover, predictor corrector schemes are suggested, again motivated by the new monolithic system. Key implementation aspects are discussed, and a complete stability analysis is performed. We end with a set of numerical examples in order to compare these methods with classical pressure correction schemes.