klaus is correct.
and the tire is unlikely.

i just fixed a shimmy/wobble that occurred on my car during braking. i thought it was my old rotors, they are 270k+ miles and the pads were well worn. i repaired/replaced the brakes and found a cracked control arm bushing on the front AND a worn out rear-shock mount on the opposite side of the car.
worn/cracked/bad bushings can make all sorts of weird driving things happen.

check for any play from any wheel.
good luck!
--
-woodsy; 280k 1995 850 wagon;