I have 17" R104s, but I wanted to put some winter tires on, and I can get a set of 15" R81s cheap. Any reason I would not want to put these on? Mechanical or aesthetically?

The winter tires would be Continental ExtremeWinterContact.
A related question is tire size: 195/60R15 or 175/65R15 on the 15" R81s?

 

Coopers came standard with 15" but Cooper 'S' came with 16" and had larger diameter brake disks on front.

There could be a clearance problem with most 15" Rims, if you have the 'S' model.

 

If they fit your car (non-S), the 15" wheels ride nice and perform well. The Holies are the lightest stock wheel with the Spoolers not to far behind and the Spoolers are cheap used. You can feel the lighter weight. You will probably also feel the extra sidewall flex when you turn.

They will look a little dinky on the car since we are all accustomed to the big wheel/narrow sidewall look, but the whole package is (and must be) about the same overall diameter as the 17's.

The 175's are the stock size tire. I think the 195's will fit, but I'm not 100% sure.

 

I should have said that the R56 is an 'S' (it's always in the details, eh?)

the guy selling the R81s is now showing pictures with a tape measure indicating 16", but he's measuring from 'lip-to-lip' instead of the inside and I think that's where he's getting the extra inch from -- based on the pictures, they are definitely R81s and those are only 15", right?

So, it sounds like, as good as a deal as this might be, 15" R81s won't fit a 2007 Mini Cooper S, right?

 

the r56-S uses the r53 jcw brake upgrade and i know even some factory 16's work over those brakes but other 16's and 15's don't because of clearance issues. unless your going to put spacers, it might not fit

 

I have an R56 S and I can confirm that the '02-'06 16" X-lites (also known as V-spokes) will fit over the larger front discs on the '07 and up R56 S models. I'm putting a set of snow tires on them next week. Good luck!