  We present results from the first simulations of networks of Type I Abelian
Higgs cosmic strings to include both matter and radiation eras and Cosmic
Microwave Background (CMB) constraints. In Type I strings, the string tension
is a slowly decreasing function of the ratio of the scalar and gauge
mass-squared, $\beta$. We find that the mean string separation shows no
dependence on $\beta$, and that the energy-momentum tensor correlators decrease
approximately in proportion to the square of the string tension, with
additional O(1) correction factors which asymptote to constants below $\beta
\lesssim 0.01$. Strings in models with low self-couplings can therefore satisfy
current CMB bounds at higher symmetry-breaking scales. This is particularly
relevant for models where the gauge symmetry is broken in a supersymmetric flat
direction, for which the effective self-coupling can be extremely small. If our
results can be extrapolated to $\beta \simeq 10^{-15}$, even strings formed at
$10^{16}$ GeV (approximately the grand unification scale in supersymmetric
extensions of the Standard Model) can be compatible with CMB constraints.
