User Terminal Session Logging

I'm looking at allowing remote telnet into my server.

like any security-minded administrator, I want to log what my users type on the telnet session.

I'm using the script command to generate transcripts of the users session.

I have /etc/profile set to automatically start the script command to log user activity, and in /etc/bash.bash_logout I have a command that emails me the transcript of the users' session.

All of the above works well except for one thing:

the users can type "exit" to escape from my script logging and any commands they type won't get logged.