Danman...
These are 5" wheels with 165 tyres on 1" spacer/drums ( same track as S discs )
I was also able to run these with no spacers/flares

These are 6" wheels with 165 tyres and discs on front, spacered drums on rear

The colour of the car should also help you invision yours....lol

 Keep in mind...like Cheleker mentions....there are many different off-sets.  Some are designed for drums, others for discs etc.  Even with the drum/disc styles, there are more off-sets. My 6" Mambas have a different off-set than my 6" Mercury's ( pictured )

Would that be the set I have, or another..lol

If you want 5s I have Cosmic MkIIIs 4-sale. I have 6 total for the price of 4. I am aware of only 1 other set in North America.

one more suggestion and I'm out of here. Don't waste your time with honda brakes. Buy the new Cooper S kit and be done with it. There are some wheels that don't clear the honda brakes and it's a dodge at best. This is an opinion.

CTR

I have drums all the way around right now but I may try the Honda front disc conversion eventually. Can you guys share some pictures of your cars with info?Thanks. 

Spitz, Chuck, malsal it's all good. I posted on another thread this morning when I say "never" someone shows me the exception. As we mature for lack of a better term I find I like 4.5 wheels with 165 tires and no flares. I also like 5 inch wheels with 145 tires. Again no flares. When I drive my lawyers car 79 with 6 inch minilites, 165 Falkins, new springs and shocks, W& flares I love it. I have several sets of 12 inch wheels and tires 145 and 165 to try on my car just to see what I think. I think this will make 11 sets of wheels and tires I have bought for this car. There is one more set I'd like to try and I think the crazy will end there. That's 4.5 S offset minilites with 165 Falkins. I'm still a ten inch kind of guy.

CTR

Danman2540, if you are running discs yes a 5" wheel will work better, with drums you should be able to run 6" wheels with the small Mayfair flares and suspension in good condition. Remember this nothing is set in stone and different wheels create different problems but the 5" wheel is always a safer bet.

CTR, maybe another way to put it is that there is no certainty that one can throw 10 X 6" disc brake offset wheels on the front of a Mini with S-disc brakes and have them clear. (Same problem with 5" drum brake offset wheels on the same S-disc brakes.) They can all be made to clear.

No need for 6" wheels on a street Mini anyway.

(Steve...my "trim what" question was at the OP....you and I were posting at same time ...although your answer helped)

I run 10x6 with 7.5" discs andYoko 032's.  I have the car lowered some and I autoslalom it.  I've not rubbed yet.

How about this?  If I go with 10x5 can I go as low as I want?

I was told the cones are pretty new but it looks like it sits low. I have the small plastic flares with exposed screws. It's not the first thing I'm doing, but it is on my list of mods so I wanted to gather info on it. 

OK, lets try this. If you buy the 6x10 wheels fit them with a nice set of 165/10 tires. You can raise your ride height or lengthen your tie /strut rods and avoid contact with the body. This may or may not be an issue depending on wheel selected, ride height and positon of sub frame in body. In cae of erection lasting more than four hours contact your doctor if you can't think of anyone else to call.  

CTR

CTR most 6 inch wheels are wider in the offset so how would that make them rub as apposed to any other wheel ? I ran 10x6 wellers with 165's and S discs on my pick up with flares and there was no trimming. I agree more info is required to give a complete answer and a lot will depend on the age and condition of the suspension components and what type of brakes he is running.

I guess I should try and be clear. If running S disc brakes, 6x10 wheels and 165 tires on the front of your car. When lowered to a two finger above the front tire spacing maybe when turning, the tire might rub. This rub may happen at the point where the front valance meets the front wings. You may also find that when running non spaced drums on the rear with above mentioned wheel tire combo the tire might rub the hand brake cable or rear swing arm. Perhaps more info is required to get you a correct answer. If you decide on 5x10s I have several sets I'd like to sell all priced according to condition.

CTR 

Trim what?...not sure why you'd need to trim anything with 10" wheels.

These are 6" wheels on non spacered drums

also...6" on non spacered drum ( different style wheel )

no pics of the front.

Am I the only one who finds it funny the first thing a new mini owner wants is bigger wheels? The answer to your question is yes and no. If willing to ride high a 10x6 wheel with 165 tire will clear but come very close to the body. Depending on how well centered your sub frame is you may have a little rub while cornering in one direction. When you decide to lower the car (the next thing new owners want to do) the tires will rub just where the valance meets the wings. If doing body work I remove 3/4 inch at that point and radius each side 6 inches to zero and restore the lip. Done correctly few can tell and you can go low as you like and swing most 6 inch wheels (disc brake rear spacing) and 165 tire. Do you plan to run flares? with 5 or 6 and 165 tires you will need flares to cover.

On the race cars we run low enough that we radius the front and rear openings all the way around about 1 inch at the top and feather to zero fore and aft.

CTR

If you have discs you should need flares to cover the tires on a 10x6 rim, if you have drums they work ok without flares.

EDIT : No trimming is required with stock suspension in good shape.

I just got my first mini and I have what I think are 4.5 or 4.75 wide mini lites.  I like the look of the 10x6 mini lites but don't want to trim my body. So can anyone tell me if I can run the 6's without trimming or if I'll have to go with 5's?