How to speed up marching cubes?

I'm using this marching cube algorithm to draw 3D isosurfaces (ported into C#, outputting MeshGeomtry3Ds, but otherwise the same). The resulting surfaces look great, but are taking a long time to calculate.

Are there any ways to speed up marching cubes? The most obvious one is to simply reduce the spatial sampling rate, but this reduces the quality of the resulting mesh. I'd like to avoid this.

I'm considering a two-pass system, where the first pass samples space much more coarsely, eliminating volumes where the field strength is well below my isolevel. Is this wise? What are the pitfalls?

Edit: the code has been profiled, and the bulk of CPU time is split between the marching cubes routine itself and the field strength calculation for each grid cell corner. The field calculations are beyond my control, so speeding up the cubes routine is my only option...

I'm still drawn to the idea of trying to eliminate dead space, since this would reduce the number of calls to both systems considerably.

I know this is a bit old, but I recently implemented Marching Cubes based on much the same source. There is a LOT of inefficiency here. At a minimum if you were doing something like

for (int x=0; x<densityArrayWidth; x++)
  for (int z=0; z<densityArrayLength; z++)
    for (int y=0; y<densityArrayHeight; y++)
      Polygonize(Gridcell, isolevel, Triangles)

Look at how many times you'd be reallocating the edgeTable and Tritable! Those immediately need to move out to the overall class. I ditched the gridCell object as well, going directly from the points/values to the triangles.

In short it isn't just the algorithmic complexity, memory allocations (and in the base this does a huge amount of them) take time also.