Authenticate root directory, but disable authentication for somesub-directories

I am not very familiar with configuring .htaccess, but I am able to
setup Basic authentication by placing the .htaccess file at the root
level of the web site.

There are about 18 root level directories that need to be
authenticated using this .htaccess file.

However, there are 2 directories that need to be accessed directly
without authentication. I've tried using mulitple <Files> directives
which didn't result in much and the <Directory> directive which was
'not allowed here' according to the server log.

Any help is greatly appreciated.

Thanks,
Dan