  Gribov copies of the vacuum in two dimensional compact U(1) lattice gauge
models are constructed. On the basis of this a gauge fixing algorithm is
developped, wich finds the minimum of the sum of link field squares. Numerical
experience in a two dimensional Higgs model with fixed length scalar field is
reported and the extension to three and four dimensional U(1) and four
dimensional SU(2) gauge theories is briefly discussed.
