  We examine the statistical properties of defects formed by the breaking of a
U(1) symmetry when the Higgs field has a power spectrum $P(k) \propto k^n$. We
find a marked dependence of the amount of infinite string on the spectral index
$n$ and empirically identify an analytic form for this quantity. We also
confirm that this result is robust to changes in the definition of infinite
string. It is possible that this result could account for the apparent absence
of infinite string in recent lattice-free simulations.
