I have a web host for one of my sites that overrides all URL's that begin with /admin or /user. Why both, I don't know, but they redirect both of those to their own administration console login.

That kind of throws a monkey wrench in setting up Drupal, which when using Clean URL's requires both of those and will conflict with the host redirect.

So, I found a little known trick of URL rewriting in Drupal 6 to cause both of those URL's to change for the entire site. Add the following lines to the bottom of your settings.php file:

function custom_url_rewrite_outbound(&$path, &$options, $original_path) {
  // Change all 'admin' to 'adm'.
  if (preg_match('|^admin(/.*)|', $path, $matches)) {
    $path = 'adm'. $matches[1];
  }
  // Change all 'user' to 'usr'.
  if (preg_match('|^user(/.*)|', $path, $matches)) {
    $path = 'usr'. $matches[1];
  }
  if ($path == 'admin') {
    $path = 'adm';
  }
  if ($path == 'user') {
      $path = 'usr';
   }
} 

function custom_url_rewrite_inbound(&$result, $path, $path_language) {
  if ($path == 'adm') {
    $result = 'admin';
  }
  if ($path == 'usr') {
    $result = 'user';
  }
  if (preg_match('|^adm(/.*)|', $path, $matches)) {
    $result = 'admin'. $matches[1];
  }
  if (preg_match('|^usr(/.*)|', $path, $matches)) {
    $result = 'user'. $matches[1];
  }
}

After that quick fix, your Drupal site will now use /adm and /usr for the appropriate subdirectories.