The brief
The owner described the rear of the A4 feeling 'floaty' over speed humps, a soft clunk over expansion joints, and rear bounce that took an extra cycle or two to settle. Daily-driver complaints, the kind you live with for a while before it dawns on you the car is no longer composed at the back.
All of it points at the rear shock absorbers. They are there to do two jobs: hold the body steady after a bump, and damp the bounce so it settles in one cycle, not three. When the damping inside them fades, the body floats, expansion joints come through as a clunk because there is slack to take up, and the back end keeps bobbing after a bump. Left long enough, that uneven rear-axle movement starts eating tyres and stretching braking distances, so it is worth doing before it gets there.
The diagnosis
On the lift, the workshop tested both rear shocks by hand. The rebound damping, the part that controls how the body returns after a bump, was almost gone on the right side, and the left was not far behind. No fluid weep, the seals had not let go, but the internals were past their useful life.
Replacing one and leaving the other would leave the rear axle loaded asymmetrically, one corner controlled, the other floating, which makes the car drive worse, not better. So it was a set job, both rear shocks together, with fresh bump stops, boots and top mounts since those are disturbed for the swap anyway and an old top mount on a new shock is a weak link.
The work
Removed both rear shock absorber assemblies. Fitted a matched pair of new Audi-spec replacements, with fresh bump stops, dust boots and top mounts, and torqued the upper and lower mounts to the workshop manual values.
Then rolled the car off for a settle cycle, bouncing the suspension to seat everything, followed by a quick alignment check to confirm the rear geometry was still where it should be after the work.
The outcome
The rear end planted again, settling cleanly. Expansion joints absorbed in one cycle instead of three. No clunk.
The A4 went home with the back end behaving like the front. For the owner, the practical win is a car that feels composed end to end again rather than loose at the back, plus rear tyres that will wear evenly now that the axle stays planted.
That is a repair you notice from the first drive out of the workshop.