Much stress and excitement this morning trying to get my new monitor to work properly alongside an existing monitor, when they're at different resolutions (the new is 1920 x 1200, and the old is 1600 x 1200). The way to get it working with Ubuntu 64-bit (Intrepid) seems to be this:

• Disconnect the smaller monitor leaving only the bigger one plugged in, and reboot.
• Ubuntu correctly detects the new monitor, and configures its resolution correctly. Set the refresh rate if necessary in the Screen Resolution applet.
• Hot-plug the old monitor, then do Detect Displays in the Screen Res applet. It will detect the smaller monitor correctly, but shows it as "Off"; Select "On".
• The applet will ask for permission to change some settings (presumably writing to xorg.conf). Agree and authenticate.
• Reboot, or restart X, and the two monitors will now work happily together.

There were some wrinkles:

• Doing this disabled the fglrx properietary AMD driver, which turns off desktop effects (Compiz). I may try turning the driver back on, and the effects back on, later today, and I'll report on whether that works or not, but if it doesn't I can live without wobbly windows.
• The larger monitor is the main monitor, and so I had to move it to the left position to get the desktop to work right. There's no easy way to swap them around in software without the ATI Catalyst Control Center applet, and that won't work without the proprietary driver (see above). So I've moved the monitors physically rather than trying to do this with software.