Vehicle powertrains with a continuously variable transmission (CVT) have a large freedom in controlling the engine speed and the torque at the wheels. Due to rotating inertias within the engine and transmission, the response of the vehicle during large engine speed shifts may appear reluctant or even counteractive. To overcome this behaviour, the CVT is augmented with a planetary gear set and compact steel flywheel. The new transmission seamlessly combines two contradictive features: the driveability in terms of the pedal-to-wheel response is greatly improved and a large leap towards optimal fuel economy can be made. This can be achieved by cruising the vehicle at extremely low engine speeds which is possible by the large ratio-coverage of the CVT. The latently impassive pedal-to-wheel response that normally would emerge is now eliminated by the gear set and the flywheel. In this paper two control strategies for the engine throttle valve and the CVT ratio shift speed are presented and analysed. The control laws are able to realize high driveability and fuel economy at the same time. Results from simulations will be discussed.