An internal combustion engine includes a cylinder block defining first and second cylinders, and a cylinder head coupled to the block. The engine also includes a passage having a first outlet and a second outlet for exhausting post-combustion gasses from the cylinder head. The engine additionally includes a mechanism for selectively activating and deactivating the first cylinder and a turbocharging system having a low-flow turbocharger and a high-flow turbocharger. The low-flow turbocharger is driven by gasses from the first outlet and the high-flow turbocharger is driven by gasses from the second outlet. The turbocharging system also includes a first flow-control device that directs the gasses via the first and second outlets to the turbochargers when the first and second cylinders are activated. The first flow-control device also directs the gasses via the first outlet only to the low-flow turbocharger and blocks the second outlet when the first cylinder is deactivated.