This modification only applies to S4s with T2 differentials (model year 2000+.) '99 S4s and older European models can be either T1 or T2. If you have one of these cars, you'll have to remove the differential from the housing to find out what type it is. If it's T1, this walkthrough isn't applicable.
The part numbers for T2 differentials:
01E 409 751 E
01E 409 751 F
First, you must remove the differential from the transmission and diff. housing. This procedure is outside the scope of this DIY. For help, see this guide for the B5 A4 or this guide by StaSIS.
Materials:
Aftermarket washers
6-32 tap
3x 6-32 threaded bolts (get a few extras, these tend to get broken)
Hammer
Vice grips or similar
Once the differential is out of the car, the spirol pins holding everything together will have to be removed. These are meant to be single use, but when removed with care they can safely be reused. Use a 6-32 tap to thread all three pins.


Next, thread your 6-32 bolts into the spirol pins and grab them just inside the heads with your vice grips. Using the hammer, hit the vice grips to tap the pins out of the differential like so:

Once these pins have been removed, the rods holding the gears on the unit are free to slip out. Be careful not to let this happen! Tape can be applied over the holes to keep them in for the time being.
Removed pin:

Once all three pins have been removed, the differential and gears must be marked for later reassembly. Each gear will have to be put back in its original location with the correct orientation. One easy way to do this is to stick a piece of tape on the differential housing next to each gear. Next, find the imprinted letter E on each gear in between the teeth and mark its location on the tape. Then, mark each window or opening on the differential housing with a number 1-3. For example:



Next, remove the rods on which the gears turn.

Wrap each gear in tape and label its location (top/bottom and window number):


With the gears removed and labeled, only the guts of the differential remain. This is the washer stack, the part we will be modifying. Pull it out, and keep the washers in order like so:



In top to bottom order, the stock washer materials and rough thickness measurements should be as follows:
* bronze - 1.96mm (can also be teflon coated instead of bronze for T2 version # 01E 409 751 E, but the sizing is identical and it doesn't change the mod)
steel 4.14mm
GEAR
steel 1.56mm
* teflon coated 1.96mm
steel 1.58mm
GEAR
steel 4.74mm
steel (darker and slotted) 1.98mm
steel 4.78mm
The hardened steel aftermarket washers replace the bronze and teflon coated washers, marked with *s in the above list. Simply swap them out and reassemble! Once the gears are back on but before the spirol pins are in, make sure the gears turn relatively smoothly (i.e. don't lock up, there will be some friction since at this point the diff. isn't lubed.)
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