bash woes

[Jonathan Matthews <jaycee@jaycee.uklinux.net>]

Ok - can someone explain the following:

jaycee@kanyon:/tmp$ ls
jaycee@kanyon:/tmp$ rm abc
rm: cannot remove `abc': No such file or directory
jaycee@kanyon:/tmp$ rm abc 2>err
jaycee@kanyon:/tmp$ cat err
rm: cannot remove `abc': No such file or directory
jaycee@kanyon:/tmp$ rm err
jaycee@kanyon:/tmp$ rm abc 2>&1 > err
rm: cannot remove `abc': No such file or directory
jaycee@kanyon:/tmp$ rm abc 2>&1 > /dev/null
rm: cannot remove `abc': No such file or directory

Why can't I silently discard the output of rm?
Am I missing something subtle?
Something obvious?
A vital brain part?

cheers,
jc