Consider a battery limited energy harvesting communication system with online power control. Assuming independent and identically distributed (i.i.d.) energy arrivals and the harvest-store-use architecture, it is shown that the greedy policy achieves the maximum throughput if and only if the battery capacity is below a certain positive threshold that admits a precise characterization. Simple lower and upper bounds on this threshold are established. The asymptotic relationship between the threshold and the mean of the energy arrival process is analyzed for several examples.