Install USB Overdrive and you'll be able to tame your mouse, so it fully meets your needs:
The USB Overdrive is a device driver for Mac OS X that handles any USB mouse / trackball / joystick / gamepad / media keyboard and any Bluetooth mouse from any manufacturer and lets you configure them either globally or on a per-application, per-device basis.
It works in Mac OS X 10.4 (Tiger), 10.5 (Leopard) and 10.6 (Snow Leopard) in both 32-bit & 64-bit.
It reads all kinds of wheels, buttons, switches and controls and assigns them to useful actions like clicking, typing, scrolling, launching, opening documents and so forth. The USB Overdrive can easily handle several USB devices at once and can assign different settings to each one.
Please note that the current version 3.0.1 is newer than version 10.4.8 even though obviously 3 is smaller than 10. I went back to a more standard version numbering scheme after I found out that trying to match the current OS number was very confusing for end users.