The exact positioning of pitch peaks often has communicative significance, but the meanings and functions this conveys have never been systematically studied. This paper reports an exploration of one basic aspect of this in one language. The phenomenon is that of "disaligned pitch peaks," that is, peaks which, contrary to the usual tendency, are not aligned with a strong energy peak. The language is American English, as used in naturally-occurring two-person interactions. To find examples, I developed a model to automatically estimate the extent to which a speech signal exhibits a strong pitch peak that is not aligned with an energy peak. Examination of examples revealed many associated pragmatic functions, including suggesting, grounding, agreeing with reservations, implying, and expressing liking, most of which have not been previously noted.