  We present a method for the introduction of small-scale structure into
strings constructed from products of rotation matrices. We use this method to
illustrate a range of possibilities for the shape of cusps that depends on the
properties of the small-scale structure. We further argue that the presence of
structure at cusps under most circumstances leads to the formation of loops at
the size of the smallest scales. On the other hand we show that the
gravitational waveform of a cusp remains generally unchanged; the primary
effect of small-scale structure is to smooth out the sharp waveform emitted in
the direction of cusp motion.
