Making a show of conceding by using a three-part structure of proposition, concession and reassertion has the effect - in contrast to other ways of conceding - of strengthening one's own position at the expense of a counter-argument. This three-part structure can be also exploited so as to carry the battle to the enemy, as it were, and make the concession do more offensive work. We detail three such ways: Trojan Horses where the speaker imports a caricature of the opposition into the conceded material; stings in the tail, where the speaker specifically overturns the concession they have just made in the original claim; and cheapeners, where the speaker works pragmatically to devalue even a positive endorsement of the opposition's case. In all their variety, what marks the concession as being hearably in the speaker's own interest is the robust, normative three-part proposition - concession - reprise structure. It is available for use in supporting or demeaning any position, whether mundane or explicitly ideological.