Could be a good start to the 2 pixel puzzle.I know Mahvin showed the best way with curves, but there has to be a way to select a stroked 3 pixel path and delete some of it's width.Even a squiggly line . polygon, or circle.
I know much of this can be done with select/shrink and select/grow, but not by .5 lowest is 1 pixel.
If a script could be developed to offset by .5 (half a pixel) and up to that objects size, that would be awesome.
Then you could select the path, shrink ,grow, or offset by .5 and either delete,fill, or grow.
A lot of possibilities for a script like that.

Also it would be nice to be able to offset the size inward, outward, or both.
Is it possible to scale an object down with the scale tool by 1 pixel or .5? I haven't really ever tried.