This paper adopts the perspective of lexico-constructional pragmatics to consider pun of traditional rhetoric as a pun trigger, and regards pun in the true sense of the term as a pun construction. In terms of sound, form, meaning, and effect which are four essential pragma-rhetorical parameters, pun constructions fall into three categories: the {X + same sound, same form, varied meaning and effect + X} pun construction, the {X + same/similar sound, similar form, varied meaning and effect + X} pun construction, and the {X + same/similar sound, varied form meaning and effect + X} pun construction. With regard to pragmatic effects, it is found that in addition to what has been addressed in earlier studies, such as humor, novelty, and association, pun construction can be employed to present the rhetor’s emotional attitudes, to circumvent excessive frankness, to deliberately misinterpret an utterance, or to downplay embarrassment. The paper also addresses semantico-pragmatic ambiguity, inheritance, networks, and the pragma-rhetorical effects of pun constructions.