That jittery, hard to keep in the same lane problem is often caused by something that is causing a very stiff ride.

Getting to recommended tire pressure which is on your door jam and also on the tire is the first thing to do. Unless the tires you are using are not recommended for your vehicle they are unlikely the cause. If the tires are under or oversized, sidewall to hard or too soft they will be a problem but if there are in spec tire to tire will feel different but should not be the culprit.

Alignment can also cause the problem. There are good and bad alignments. I would have it checked to make sure it is within BMW specs or has gone out of alignment.

If it has gotten worse over time and your suspension has 75,000 miles or more of wear there are several components that could cause your problem. I would have it thoroughly checked over even if it is not toward the end of normal life cycle.

Generally the problem is magnified the faster you go. If it is in the steering the vehicle won't feel jittery but will wander at slow speeds. Steering problems hit my critical to fix ASAP list.

Some roads will cause that feeling when all is OK. In your case if you are more than 5 pounds over inflated I think it is at least contributing to the problem by losing some of the cushioning the tires do and perhaps losing some of the tire patch.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas