convert -size 20x20 xc:#eeeeee test.png
Produces this:

Interestingly, I get this effect for grays - put in another colour like #eeeeef, and it's fine.
On the gif front:
convert -size 11x21 xc:transparent test.gif
gets me this:

If I increase the size to 12x21 or 11x22, it's fine, and I just get a transparent gif.
I'm finding this confusing (and it's causing me a lot of headaches) - but it's consistent across several machines, on Windows 7, and 2003 Server.
The gif bug was present as early as 6.6.3 - possibly earlier.
Any suggestions would be very much welcomed.