Hybrid vehicles and methods of operating the same are disclosed. Example methods may include providing a powertrain for the vehicle, which includes an internal combustion engine configured to provide rotational power to a rotatable input of a transmission by way of a starting device, and an electric motor-generator comprising a rotor configured to selectively provide rotational power to the rotatable input. The method may further include selectively disconnecting the engine from the rotatable input using a disconnect device separate from the starting device, thereby allowing the rotatable input of the transmission to be driven at a speed faster than an output speed of the engine.