  For an asymptotically free theory, a promising strategy for eliminating
Critical Slowing Down (CSD) is na\"ive Fourier acceleration. This requires the
introduction of gauge-fixing into the action, in order to isolate the
asymptotically decoupled Fourier modes. In this article, we present our
approach and results from a gauge-fixed Fourier-accelerated hybrid Monte Carlo
algorithm, using an action that softly fixes the gauge links to Landau gauge.
We compare the autocorrelation times with those of the pure hybrid Monte Carlo
algorithm. We work on a small-volume lattice at weak coupling. We present
preliminary results and obstacles from working with periodic boundary
conditions, and then we present results from using fixed, equilibrated boundary
links to avoid $\mathbb{Z}_3$ and other topological barriers and to anticipate
applying a similar acceleration to many small cells in a large,
physically-relevant lattice volume.
