*Smallest* rim that will fit on an 03 330xi?

[MechE00]

I'm checking my options on getting a second set of rims to mount snow tires on for a recently purchased 330xi. Since 17 inch rims and tires tend to come with a significant step up in price over smaller sizes, and I am more concerned with safety than hard driving when I am using snow tires, I am curious to see if anyone knows whether there are smaller sizes that will clear the brakes.

If you have experience with a specific rim, please mention which type, etc. in case some will fit, and some won't...

thanks...