Under Real Time Pricing (RTP) rates, Electric Thermal Storage (ETS) can be used to shift electricity consumption away from higher price periods to lower price periods. Conceptually, this is similar to the function of ETS under time of use (TOU) rates. However, under RTP, because of variability of prices and absence of demand charges, ETS charging can occur at any hour of the day and energy can be stored across several days. This paper addresses the issue of storage sizing under RTP rates by presenting the results of a simulation study. Parameters of the simulation, as well as building loads and prices used as inputs, are based on the results of an actual experiment on the RTP based control of ETS carried out in the winter season of 1989-1990. Results indicate that under RTP based control, increase in storage sizes lowers utilities' cost of service, in contrast to TOU based control where utility's cost of service remains relatively unchanged.