Two methods may be used to start the engine of a hybrid electric vehicle while the vehicle is moving under electric power. When smoothness is most important, a disconnect clutch is partially engaged to initiate engine rotation and then released as the engine accelerates under its own power toward a motor speed. When rapid starting is most important, the disconnect clutch torque capacity is controlled to decrease the time required for the engine to accelerates to the motor speed. A torque converter bypass clutch is disengaged during the engine restart under either method. Also, the motor torque is adjusted under either method to compensate for the torque provided to the engine.