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Spin-transfer-driven switching is investigated by micromagnetic simulation in perpendicular spin valve nanopillars with a free layer structure which contains two in-film-plane regions: a main perpendicularly magnetized hard region and a soft nanocore with intrinsic in-plane anisotropy. The temporal magnetization snapshots demonstrate that the current-induced magnetization rotation starts from the nanocore, followed by an incoherent switching process mediated by domain nucleation and expansion. The initial magnetization rotation of nanocore to in-plane direction generates driving force acting on the hard region via exchange coupling, together with locally enhanced spin torque, leading to considerable reduction in both critical current and switching time.