DB connections ?

Hello, I am designing a web that will require access to a specific database. I am also using sessions and am storing the session data in the database. So on every page that loads there will be a connection to the mysql server (local) to access the session db and tables and the web app database and tables. My question is this would make two db connections per page right ? one after another ? -- which would not be optimized ?? Would it be better to but the session tables in with the web app tables under a common database ?? At first I thought that it would be more secure if the two where separate. Any comments ... Michael.