I still say put it on a lift and get under it and listen with a scope. It doesn't need to go fast just in 1st gear maybe have someone hold a wheel while the other spins.

Thanks , Mike
I would have noticed a loose wheel stud having taken the wheel off umpteen times

have tried 3 different sets of pads,
with/without rubber backing,
with/without back plate anti-squeal goo,
with/without back plate lubricant (not grease)
have also flipped pads inner to outer side of caliper (but not to other wheel)
I think I have exhaustively excluded pads themselves as the problem

yes swapping rotors would at least give the diagnosis if the sound went to the other side
Harvey

what about a loose wheel stud?  and maybe try swapping first the pads to the opposite side, then swap the rotors to the other side.

Rotor: No wobble, no high spots, no pulsating, no scoring , inner and outer faces look fine. Yes, there could be flaws inside the metal. I had that happen once on a Ford when there was a hard spot inside a rotor that was not known until  40,000 miles of wear exposed the hard lump.

centering the caliper? - actually it can be done , although I have read nothing about that.  - My rotor is not on-center exactly and is within .030" of the caliper slot inner side, but the rotor is not touching/ not scored. The other side it just like it. Could it be centered? Yes - I bought some SS washers. Have not installed them . Actually bought two shapes: standard washers and fender washers. The latter would provide a larger/more stable surface area but would need to be trimmed to fit

the caliper mounting bolt would go through : dust shield ear- caliper- new "spacer" SS washer - mounting boss.
The new spacer would move the caliper inwards.

 I did remove the caliper and look around. While I was in there, I did try to install the new SS spacer, very fiddly and I did not try very hard as it was not necessary anyway.  If doing it for real,  I would first glue the SS washer onto the caliper or the mounting boss before attempting to put it all together.

Caliper rebuild kit ordered. I doubt if I have any followup for a month or two.

I'd remove that left rotor and get it magnifluxed. If you don't want to spend the $$ for that, get a magnifying glass and get a good look at the brake bearing surfaces inside and out.  I believe it's got to be one of the 3 moving parts. rotor, pad or piston.  Maybe also look at the caliper  and see if both pistons are tight in the caliper. Could be one of the bores is out of round and when pushing on the pad, rocking a bit, but it sounds like ,and I didn't hear the sound, a defective rotor. 

BTW  how could a rotor be not centered, or how could you center it?  I think it's only going to sit in one position and if it's off set, it's by design or an error in design.

Hank, also check the inside of the rotor and the face of the hub. Make sure there's no high point on either side that would set off a 'wobble' that could be your noise.

definitely front noise, only on braking,  and rotational

inside the car with windows up, it sounds or even feels like front wheel well

listening with window down, or by outside observer as I drive by, it sounds like pad noise grinding on rotor, Much lower pitch than I have heard on other cars. Almost palpable and felt through the pedal. 

at this point I have eliminated a pad -only problem

It is aggravating to not have a diagnosis first,
but next step is to either replace caliper (2 yr old with SS pistons)
or rotor (6 months old and worked fine until 2 months ago when noise started. 

Then again, before I replace anything, I could unbolt the caliper (not replace it), loosen the castle nut, and pull off the rotor assemble to look around incl bearings (even though the noise NOT continuous bearing noise and is pad/rotor noise only on braking.

Are you sure the noise is from the front brakes? mini's are like little sound boxes and sometimes very difficult to pin a noise down. I would suggest that you check the rear brakes as well, especially the orientation of the return springs which will produce a very growly type noise as you indicate as the problem. Secondly the offset pads will have no connection to the noise, one piston will always move before the other and as long as they both do move eventually the pressure will be the same to each caliper piston, the pressure will not change because one is further out than the other, pressure is governed by surface area of the piston not piston position. If the noise is indeed from the front then I would suggest a complete strip of the hub assembly. All this is from the comfort of my armchair and really without actually hearing and feeling the noise is about as much use as a chocolate tea-pot..........................................

Replace the caliper.  If it fixes the problem, great.  If not, at least you have a spare.

Still with me?

So I bought a third set of pads - standard Minimania pads

Drove the car one mile and a few mild stops from 30 mph, just enough wear on the pads to prove that both sides are getting pressure from the caliper pistons to the pads ( I already knew that as the car stopped straight from any speed)

These brand new pads are wearing in same rate - see photo : brand new pads with one mile and a few stops

At this point I have no idea what is causing the problem. No the dust shield does not touch. There is no scoring anywhere. The rotor "rings" solid when I tap on it and visually looks fine. No slop in bearings or suspension parts.

I figured at this point, why not try anything?

We had discussed chamfering the pads. What I meant was NOT the leading or trailing edges that sweep, but thinking radially, could the lower (or upper) edge of the pads be noisily scraping on the rusty new unswept portion of the rotor? 

At first I thought I was on to something. Look at the chipped edge of these pads.
This is the inner (lower) radial side (the one closest to center of the axle)
Yes, they looked chipped, but buffing them off AND the rusty part of the rotor made NO difference.

to continue

I measured the clearance on that off-centered rotor in the Caliper slot. It is .030" . No evidence of scoring. SAme thing on other wheel/ Bearings are tight in/out . I do not think this is an issue.

So what else to do?

I tried 2 pads with no success
EBC pads, two types, ones with and without rubber backing, plain ones with and without anti-noise goo, plain ones with and without brake lubricant (not grease)

So look at the rotor and normal rusting

here is some update

the good:
braking is smooth and straight on mild, moderate or panic braking.

(new better -quality rotors (and new pads) last fall solved a warped 2 yr old rotor problem. All was well until recently - noise is new 1-2 months. Rotor swept surfaces are not rusted, car gets driven enough to keep rotors clean)

the bad
very noisy LEFT SIDE ONLY  grinding rotor noise, not high pitched squealing, only on braking, any speed, hot or cold ambient temp or brake temp

original post showed what I thought was inner caliper piston ( 2 yr old with SS pistons) not moving normally. I was incorrect. It was pointed out that the rotor was not centered, hence the new (thick) pad pushed the piston all the way in on that side. We wondered if the off-centering was a problem. However, there was no scoring of any surface, and anyway the opposite wheel had the exact same degree of off-centered-ness and makes no noise. Left side photo repeated here :

Me too! No worries.
...
Ottawa now "here today, more tomorrow... may be gone by May". Last week, the roads, parking lots etc. were completely bare and dry enough I wore sneakers outside! Today, just got in from an hour of running the snowblower.
...
Light braking = no noise suggests the disks are straight and uncracked. Just pry the pads back to ring it like a bell.
Moderate or heavy braking with noise suggests deformation due to unequal piston pressures. Remedy: fix the caliper. With equal forces on the disk, it should run true and not be pushed sideways.

I wondered about that

the previous new rotors place 2 yrs ago were fine at first and then developed warp/pulsating (and lugnuts were not overtorqued 40ftlbs)

warp/pulsating was cured by putting in the current higher grade ones ( but not race grade).  They are smooth, but it would be ironic ( and my bad luck) if the higher grade ones had hairline cracks.

This will need to be looked at, too. I suppose taking it off the car and ringing it like a bell might detect an otherwise small defect?

have you had both rotors off the car to examine them for hairline cracks?  That surely can make a vibrations noise
and can also be hard to detect the cracks.

Dan , I am not being argumentative, but just discussing.

I fully understand the centered in the slot concept, it is just that I would expect to see a bright strip mark where any steel meets any steel through hundreds of revolutions. (rusted or not),  if that is what it is. The other option is that it is pad on rotor noise.

The snow is a spring in VA snow. Here today, gone tomorrow. I have driven mini once a week over the last 2 months in a variety of temps. Air temp makes no difference. Neither does rotor temp, cold or hot. Noise starts with the first push on the pedal, every time, same even after multiple stops. Noise always disappears immediately with foot off the brake. Very light braking no noise, medium or hard causes noise.

I will get to the bottom of this eventually . Harvey

edit: PS:I bought some SS washers and fender washers in case I find that I want to move the caliper over. Anyone do this? I imagine there needs to be enough surface area of the (two ) washers so the caliper will not be " wiggly." Anyone ever do this? 

... because the new rotors aren't centred relative to the notch. Every part that was ever made had manufacturing tolerance. On a brake disk, it isn't as fine as other parts. The surface of the new disk that meets up with the drive flange may be 1-2mm closer or farther way from the plane of the main part of the disk, resulting in it being closer to one side of the notch than the old one. Similarly, the mounting surface of your caliper may be a millimeter or so closer to or farther from the notch than the design distance. Now when you think about all the parts connected together between the caliper body and the disk plate (caliper, hub, bearings (and pre-load), drive shaft, drive flange and disk), that's at least 5 contact planes with two surfaces at each contact plane = 10 machined surfaces each with its own tolerance.  If each one is off by, say .3mm, that's a combined possible mis-fit of 3mm. If the (hypothetical) acceptable tolerance for each surface is 0.1mm then the overall acceptable tolerance would be 1mm.  That's a "plus or minus" tolerance. However, I doubt cast items such as calipers, hubs, drive flanges and brake disks get quality assurance testing of each piece coming off the line. Maybe 1 in 100. So the potential is that any of these pieces could be out by 1mm. Add to that the variance in used, worn parts - they may be within tolerance, but the accumulated error gets too be too much.

Now, I have a question: if it is too cold/snowy to work on the car (I understand that part!) then how do you know it is actually still making noise? Maybe the issue is cold parts contracting and reducing tolerances.

great idea, although I do not know if I want to inspect that close to the moving parts and wind up my shirtsleeve!

Put it on a 2 post lift and run it through the gears using the brakes with someone underneath the car they should be able to find the noise.

This is my third reply today to all the good thoughts. Guys, I appreciate it. Keep them coming.Some of this is mental whacking off until I can get a warmer snow-melted day later this week and actually do something with the car.

I was not thinking of a trial of chamfering the leading or trailing edge of the pads (as they sweep the swept area of the rotor). Instead, I was thinking RADIALLY. If the inner or outer radial edge of the pad was scrubbing along the edge of the rusted unswept area, then perhaps that could cause noise. Of course, the original rotors were older and rusty, so why now?