  Compact U(1) theory in 4 dimensions is used to compare the modified iterative
and the Laplacian fixing to lattice Landau gauge in a controlled setting, since
in the Coulomb phase the lattice theory must reproduce the perturbative
prediction. It turns out that on either side of the phase transition clear
differences show up and in the Coulomb phase the ability to remove double Dirac
sheets proves vital on a small lattice.
