We examine the effects of price discrimination in the Stackelberg competition model for the linear demand case. We show that the leader does not use any price discrimination at all. Rather, the follower does all price discrimination. The leader directs all of its first mover preemptive advantage to attract the highest value consumers who pay a uniformly high price. We observe that profits and total welfare are larger and consumer surplus is smaller than those of the standard Stackelberg competition model.