  We derive the Bogomol'nyi equations for supersymmetric Abelian F-term cosmic
strings in four-dimensional flat space and show that, contrary to recent
statements in the literature, they are BPS states in the Bogomol'nyi limit, but
the partial breaking of supersymmetry is from N=2. The second supersymmetry is
not obvious in the N=1 formalism, so we give it explicitly in components and in
terms of a different set of N=1 chiral superfields. We also discuss the
appearance of a second supersymmetry in D-term models, and the relation to N=2
F-term models. The analysis sheds light on an apparent paradox raised by the
recent observation that D-term strings remain BPS when coupled to N=1
supergravity, whereas F-term strings break the supersymmetry completely, even
in the Bogomol'nyi limit. Finally, we comment on their semilocal extensions and
their relevance to cosmology.
