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When I do a select using the ellipse tool and bucket fill the selection, I get anti-aliased edge. When I do a select using the Fuzzy select tool and then do a bucket fill, the edge is solid. I need anti-aliased edge. Is this possible using the the fuzzy tool?
Using fuzzy select , use feather edges :
[attachment=6054]
Thanks. Feather edging doesn't quite do what I need. I am trying to make small simple icons and hoping for better looking edges. Feathering is a slight improvement but still doesn't quite do it for me. Here's an example. Left circle: ellipse anti-aliased select and filled. Middle: ellipse non-AA select and filled. Right: fuzzy select on middle with a feather radius of 2 and moved the selection outline to right and filled.

[attachment=6057]

The free-select tool works as well as the ellipse tool. But, the shapes I am working with is too complex for the free-select tool. Hence I am hoping the fuzzy tool would work. Doing AA manually is possible but it's very hard.
All small images as your example ? What you can try.

1) Increase the fuzzy select threshold. The default is 15 bump it up to 50 or 60 (experiment)
2) After moving the selection and filling grow the selection by a couple of pixels just to contain the next bit.
3) Apply an anti-alias filter. Unfortunately the Gimp version Filters -> Enhance -> Anti-Alias is a bit limited. Try the gmic_gimp plugin http://www.gmic.eu There is a Windows installer there. A bit over-kill but there are a couple of alternative anti-alias filters to try.
4) Kill the selection.

example: https://i.imgur.com/Gljpg5o.mp4
Let me restate what I am trying to do. Suppose I come up with the design on the left. The jagged edge is unattractive. So, I want to smooth it through anti-aliasing. I use the free-select tool to outline my design as shown in the middle. I then move the selection outline to right and fill it. The bottom right corner shows the rendered difference between the original design and the improved one.

GIMP is extremely sensitive to where I place the connecting spots when using the free-select tool. It would come up with different anti-alias fading depending on the location of the spots. Even if a spot is moved by 1 million-th of an inch, the anti-aliasing would be different. This means I have to manually reprocess the anti-aliasing. Is there a better way? I suppose this way is still 100x better than doing the edge fading by hand, which was what I was doing until I stumbled onto this earlier. You can see on the right, the anti-alias is different between the left part and right part of the image. This is because I am not a bot and unable to place the connecting spots with precision to the million'th decimal places.

[attachment=6059]
No need to re-state. You want to introduce anti-aliasing in a pixel graphic.

Two more ways.

1. Select and copy the graphic. Paste and get a floating selected layer. Scale the floating selected layer up 200% Scale it back down to 50% ( original size ) Scaling interpolates the pixels and introduces anti-aliasing.

2. Probably the best way
Make the selection. Make a path from the selection. Selection off. Move the path to required location. Edit -> Fill Path.
example: https://i.imgur.com/piDOiaR.mp4
Thanks. The scale up down technique introduces quite a bit of "noise" on the edge, resulting in visual distortion. The above-described free-select technique gave a crisp result, especially when I use mirroring to fix the asymmetric anti-aliasing.
I gave the selection to path a try and it seems to do what I need. Can't say I understand the concept behind it. But if it works, I am happy. Thanks a lot for the help.
Rich, this one is aggravating me.  I followed your directions, seemingly to a T, and can't reproduce the results.  The path is just as jagged as the original image.  Can you figure out what I am doing wrong?

See here:

https://imgur.com/pH2xu9t
It is a matter of scale. The original question is about pixel-size graphics.

Using a path is about sub-pixel rendering. A path can cross a pixel and the density of the fill depends on how much of the pixel is included. Of course Gimp is a bitmap program so the minimum fill is the pixel.

https://i.imgur.com/fvwbvOJ.mp4
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