  We examine the power spectrum $P_n$ of the $n$th harmonic for
Garfinkle-Vachaspati cosmic strings, which correspond to planar rectangular
loops. While these loop tractories are self-intersecting, a slightly perturbed
non-self-intersecting form of these trajectories has been suggested as a
generic end state of cosmic string loop fragmentation. We find that $P_n$
scales as $n^{-2} \ln n$, rather than the expected $n^{-2}$ for kink-kink
collisions. This result is demonstrated analytically for even $n$ in square
loops and numerically for all other cases. At lowest order, the effect of loop
decays is to further enhance $P_n$ at large $n$ relative to its value at small
$n$. The consequences for relic stochastic background radiation along with the
caveats pertaining to our results are discussed.
