Your description sounds like the tires twisting and sending the steering wheel back to center. If you have slop in the steering it won't return to the same place from both directions.

Eg. Turn right with a few oz of force and It will stay where you left it. Turn left and likewise will stay left of where you started. A "dead zone" that you must cross over any time you go from left to right.

The jiggle you describe could be from a number of things like CV or rotors and it is not normal so something is worn. It's so subtle I doubt highly it will cause wear just use a string to check your toe alignment front and back. Both sides.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)