BTW Archer, what do you mean by "thinning the edge"? I've heard this term used in different ways with regard to reprofiling. Do you mean to resharpen at a shallower edge bevel angle (say, going from 20 degrees to 15)? Or do you mean adding relief bevel? Or what? Thanks.
A thinner edge means there is less drag as you slice deeper into a cut. A thicker edge means that the stock gets thicker quickly after the edge, creating drag which makes deep slicing cuts a bit harder to do. Thick edge =stronger for impacts vs a thin edge.
Since I convex my Busse edges (using the same steps in the BRKT link in my last post) it would mean I shallow the edge bevel. If I had to eyeball, I'd say I convex my small blades at 12-15 degrees/side with a few finishing swipes (never more than 2 at low grits) at a higher edge angle, say 30 degrees, to remove any burr - not necessarily enough to create a secondary bevel. I then always strop with hanging loaded leather.
For a chopper, I convex at maybe 15-20 degrees.
The down-side to convexing at a low angle is that you are actually removing some of the edge shoulders - and on a Busse that means removing some of the finish. I think I posted this elsewhere (going by memory here), but an example would be that on one of my edges I have almost 4 mm of visible polished edge, instead of the 2 that came from factory.
If I got a unevenly ground edge, I'd probably start with low grit wet/dry sandpaper like 200 until the edge was even, then work my way up through higher grits (400, 800, 1200, 1500, 2000). Unfortunately I haven't yet found higher grit paper in my neck of the woods, but even then I can get a pretty wicked sharp edge at 2000 grit; and stropping regularly makes all the difference.