the way I'm looking at the problem is more like if we have 3 colors, a light, medium and dark, the dark and the light can't touch, except for the corners, and you have to bridge the colors using the medium color. Problem with this is that i feel like I've seen a lot of good pixel art where you have a really bright highlight, and to 1 side you have smooth blending, but to the other side you have the darkest color in the palette. I'm not sure if this is a lighting thing, a style thing, or what, if anyone knows, please let me know 
If you look at the second image I posted you'll see that I've put the light and dark together. The trick is to keep in mind that
bright plus dark equals medium, and you can take advantage of that to get rid of banding, like so:
bb
ac
bb
ab
ac
bc
(if you imagine drawing a line between the two b's in this one, you'll see that you end up between the light and the dark, which kind of cancel each other out)
instead of
bc
ab
bc
ab
ab
bc
And you can extend it in many different ways:
bab
cac
cbc
cab
cab
bbb
cab
bbb
aabcc
abbbc
aabcc
abbbc
aabcc
instead of
bab
cbc
cbc
cab
cab
bab
cbb
bbb
aabbc
abbcc
aabbc
abbcc
aabbc
And it can work for double pixels as well:
cb
cb
da
da
cb
cb
One thing to note is that you end up with coarser dithering patterns this way. The most important thing is to try and notice where you can place a pixel so that it looks best. After a while, you'll begin to see a pattern.
