How do you add files to an existing compressed tar file?

[Erik Bixby]

I can successfully create a tar file with something akin to

tar -czvf /path/to/archive.tgz /path/to/file/to/backup

Once the archive.tgz file is created, how does one add another file to
it?  Everything I've read gives me the impression that

tar -rzvf /path/to/archive.tgz /path/to/other/file/to/backup

should work.  However, that's blowing my archive.tgz file up.  Any ideas?

What I'm trying to do is write a script to create archive.tgz if it
doesn't exist (works), and add a file to it, if it does already exist
(currently blows up my archive).
-Erik