Previous research shows an anti-primacy effect (Bailenson & Rips, 1996), in that the first speaker in a conversational argument incurs more Burden of Proof (BOP) than the second speaker. In addition, claims may be encoded differently when they are embedded in a structured dialogue than when processed outside the context of the argument. We were interested in determining how the strength of specific claims in the argument depend on their location in the structure as a whole, and whether anti-primacy would persist in disputes where the claims offered by the two speakers were equally convincing. Subjects read interactive arguments between two speakers having a conversation, rated the convincingness and support levels of the individual claims when they were both embedded in the dialogue and removed from the dialogue, and judged overall burden of proof. Different groups of subjects saw the same arguments, the only difference being which speaker (first or second) made the particular groups of claims. The antiprimacy effect occurred even though the strength of the claims did not change as a function of which speaker presented them. In addition there was no difference between convincingness and support ratings, although the results demonstrated that the level of both types of ratings was somewhat a function of where in the argument structure the claims were situated. Specifically subjects perceived claims occurring in the initial position in the dialogue as less convincing than the same claims when the claims were removed from the context of the argument. furthermore, these initial claims correlated less with BOP than did the later claims.