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 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

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... id drop to zero at β_c, the deconfinement point, this result predicts that Dirac strings must be sufficiently dilute at β > β_c. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at β∼β_c.