  $F$-term GUT inflation coupled to N=1 Supergravity is confronted with CMB
data. Corrections to the string mass-per-unit-length away from the Bogomolny
limit are taken into account. We find that a superpotential coupling
$10^{-7}/\mcN \lesssim \kappa \lesssim 10^{-2}/\mcN$, with $\mcN$ the dimension
of the Higgs-representation, is still compatible with the data. The parameter
space is enlarged in warm inflation, as well as in the curvaton and
inhomogeneous reheat scenario. $F$-strings formed at the end of $P$-term
inflation are also considered. Because these strings satisfy the Bogomolny
bound the bounds are stronger: the gauge coupling is constrained to the range
$10^{-7} < g <10^{-4}$.
