How to prevent connection string from being public?

I'm using a MySQL database from within some Perl cgi's. To
make the connection, I have to supply the username/password
in the connection string. This info is readable for anyone
that can view my code, e.g. all other users that can access
the webserver directly, or by some possible exploit.

How can I avoid this? I can't have my own webserver, obviously.

I have set up the database server so it only accepts connections
from the webserver box, but that doesn't help with the above
problem.

Any pointers?

James