The invention is directed toward methods for operating a parallel hybrid vehicle in a manner that responds to the operator's demand for power output, while maximizing engine efficiency and minimizing disruptions in vehicle drivability. According to principles of the present invention, when the driver of a hybrid vehicle makes a demand for power output immediately after a braking event, the power provided to meet the initial demand is from either an ICE or a secondary power source. Which power source is used, and when it is engaged and disengaged, depends on various vehicle operating conditions. Also, the ICE is selectively turned off and on in response to various operating conditions.