Is it possible to use a Spyder or Eye-One to calibrate a glossy computer monitor

Are there any differences in the process from calibrating a matte finish monitor?

Bueller?

The surface finish on the monitor should not make a difference. Since when calibrating a monitor you are just reading the light being emitted from the monitor. I would be careful to make sure your ambient light is controlled to reduce any reflections. Either the Spyder2 or Display2 will work great.