Thanks for the reply.
I was doing some final tweaks to a normal map for a game object, a radio, smoothing out the colour transition in a small area within the borders of the 4 numbers in this image (there are colour differences from left to right and up and down between the numbers):
I broke the area down into 8 different sections and applied the gradient tool to each one, which helped a lot. After applying gradients, the colour differences were almost invisible on the texture except under zoom, and actually unnoticeable in-game except in one particular lighting condition - when the sun is shining just a touch from just a bit in front of directly to the side (hope that made sense).
i.e. in 99% of conditions, the radio looks similar to this:
but in that one lighting condition, the shadows result in a sharp horizontal line in the particular area I mentioned, like so:
Which corresponds exactly to a barely-visible seam in that location on the normal. (At first I thought it was the specular map.) Considering that the flaw is visible only in in such relatively rare instances, and only when the player is viewing the radio very close in, I'm not set on getting it perfect but just want to minimize it as much as I can.
It seemed to me that Gaussian blur was the perfect tool for this purpose. My initial selection included the pixels bordering right up against the outer portions of the 4 "fins" that surround the area, which contain all sorts of bright colours. The result was indeed a smoothing out of the shadow transition, but the bleeding from the fins caused a noticeable loss in visual quality in those areas so was just trading one problem for another.
I got it pretty darn close to what I wanted simply by reducing the selection area so it was far enough away from the fins. I appreciate the tips though, I may well go back and see if they'll help. I certainly never thought of turning off anti-aliasing as I've always associated AA as producing sharp edges. Although, granted, my knowledge of AA is pretty rudimentary, i.e. in gaming, you crank up the AA for sharper images and turn it dow for better performance but lower visual quality.