In this paper, we consider the optimal policy for a generator offering power into a wholesale electricity market operating under a pool arrangement. Anderson and Philpott [Math. Oper. Res., 27 (2002), pp. 82-100] recently discussed necessary conditions for an optimal offer curve when there is uncertainty in the demand and in the behavior of other participants in the market. They show that the objective function in these circumstances can be expressed as a line integral along the offer curve of a profit function integrated with respect to a market distribution function. In this paper, we prove the existence of an optimal offer stack, and we extend the analysis of [Math. Oper. Res., 27 (2002), pp. 82-100] to include necessary conditions of a higher order in the presence of horizontal and/or vertical sections in an offer curve. Finally, we establish sufficient conditions for an offer curve to be locally optimal.