Methods and arrangements for controlling hybrid powertrains are described. In one aspect, an engine is alternatingly operated at different effective displacements. One displacement delivers less than a requested powertrain output and the other delivers more. A motor/generator system is used to add and subtract torque to/from the powertrain to cause the net delivery of the requested powertrain output. In some embodiments, energy added and subtracted from the powertrain is primarily drawn from and stored in a capacitor (e.g., a supercapacitor or an ultracapacitor) when alternating between effective displacements. In another aspect a hybrid powertrain arrangement includes an engine a motor/generator and an energy storage system that includes both a battery and a capacitor. The capacitor stores and delivers electrical energy to the motor/generator unit during operation of the engine in a variable displacement or skip fire mode.