Hybridisation of vehicles is not only equivalent to improved energy efficiency and reduced emissions. In this paper, the additional degree-of-freedom introduced by electrifying the propulsion system of a vehicle is used for improving driveability. The vehicle in focus is a truck with an electric machine integrated into the engine's flywheel, a so-called integrated starter–alternator, that is, a vehicle with a low level of hybridisation. The electric machine is used to assist the internal combustion engine during transients. The idea is to use the internal combustion engine in combination with the electric machine to actively damp out oscillations induced in the driveline during acceleration. This paper includes driveline modelling, control design and verifications by simulations. The simulation shows that the use of powertrain control for a mild hybrid parallel powertrain configuration works very well. Not only can the driveability of the vehicle be improved it also reduces the emissions and is energy efficient.