The parameters for the Fattal tone mapping in the photo below are as follows:

  • Result Size: 1536×1024
  • Pre-gamma: 1.00
  • Alpha: 0.10
  • Beta: 0.94
  • Color Saturation: 0.90
  • Noise Reduction: 0.00
I didn’t change either gamma or the levels after the tone mapping operation.  Instead, I edited the image with GIMP, duplicated the layer and set the layer mode to multiply.  This worked fairly well, but for the upper half of the image ending up darker than I would have liked.  So I created a graduated selection which ran from mostly invisible at the top to fully opaque about a third of the way from the bottom.  I set this as the layer mask on the “multiply” layer.  The image looked much better.
There was a large halo around the big saguaro in the foreground just along and slightly above the horizon.  I found the exposure from the original seven used to create the HDR image, scaled it to the correct size and then copied it over as a new layer.  I created a layer mask with the halo area and then adjusted the transparency until it looked right.  The color wasn’t quite right along the horizon (and still isn’t, but it’s better), so I used curves to increase the amount of red in that area and decrease the amount of green.
I discovered that, when using Fattal, choosing the result size makes a big difference.  I had been choosing a result size of 6000×4000 which was the size of the exposures that came out of the camera.  But doing this resulted in an image that looked over-sharpened when viewed at a scaled resolution.  I tried for a long time, but failed to come up with a set of parameters which looked really good with that large result size scaled down to something smaller.  If you view the 6000×4000 result unscaled, it looks pretty good.
The image below will look best if viewed at its native resolution of 1536×1024.  It will probably not look too good if the device upon which you’re viewing it scales it to some other size.