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We present a method for the introduction of small-scale structure intostrings constructed from products of rotation matrices. We use this method toillustrate a range of possibilities for the shape of cusps that depends on theproperties of the small-scale structure. We further argue that the presence ofstructure at cusps under most circumstances leads to the formation of loops atthe size of the smallest scales. On the other hand we show that thegravitational waveform of a cusp remains generally unchanged; the primaryeffect of small-scale structure is to smooth out the sharp waveform emitted inthe direction of cusp motion.Comment: RevTeX, 8 pages. Replaced with version accepted for publication by  PR

Cosmic string cusps with small-scale structure: Their forms and gravitational waveforms