We consider an energy harvesting transmitter with a hybrid energy 
storage unit: There is an ideal super-capacitor (SC) of finite storage 
capacity and connected to it is an imperfect battery of unlimited 
storage capacity. The transmitter is free to store the incoming energy 
in the SC or in the battery. The energy for data transmission is 
drained from the SC and the battery simultaneously. We investigate 
deadline constrained offline throughput maximization problem over 
a point-to-point channel with such a transmitter. The hybrid energy 
storage model imposes a generalized set of constraints on the 
transmission policy and we show that the solution is obtained 
by application of the directional water-filling algorithm in 
multiple stages.