  Lattice discretisation errors in the Landau gauge condition are examined. An
improved gauge fixing algorithm in which ${\cal O}(a^2)$ errors are removed is
presented. ${\cal O}(a^2)$ improvement of the gauge fixing condition improves
comparison with continuum Landau gauge in two ways: 1) through the elimination
of ${\cal O}(a^2)$ errors and 2) through a secondary effect of reducing the
size of higher-order errors. These results emphasise the importance of
implementing an improved gauge fixing condition.
