  We evaluate numerically and analytically the dynamic critical exponent $z$
for five gauge-fixing algorithms in SU(2) lattice Landau-gauge theory by
considering the case $\beta = \infty$. Numerical data are obtained in two,
three and four dimensions. Results are in agreement with those obtained
previously at finite $\beta$ in two dimensions. The theoretical analysis, valid
for any dimension $d$, helps us clarify the tuning of these algorithms. We also
study generalizations of the overrelaxation algorithm and of the stochastic
overrelaxation algorithm and verify that we cannot have a dynamic critical
exponent $z$ smaller than 1 with these local algorithms. Finally, the analytic
approach is applied to the so-called $\lambda$-gauges, again at $\beta =
\infty$, and verified numerically for the two-dimensional case.
