  We derive different representations of compact QED fixed to Landau gauge by
the lattice Faddeev-Popov procedure. Our analysis finds that (A)Nielsen-Olesen
vortices arising from the compactness of the gauge-fixing action are {\it
quenched\/}, that is, the Faddeev-Popov determinant cancels them out and they
do not influence correlation functions such as the photon propagator; (B)Dirac
strings are responsible for the nonzero mass pole of the photon propagator.
Since in $D=3+1$ the photon mass undergoes a rapid drop to zero at $\beta_c$,
the deconfinement point, this result predicts that Dirac strings must be
sufficiently dilute at $\beta > \beta_c$. Indeed, numerical simulations reveal
that the string density undergoes a rapid drop to near zero at $\beta\sim
\beta_c$.
