Took the car to American Tire Discount, explained the symptoms and they put the car on the hoist. Front tyres are balanced, so no problem there. Checked the rears and the rear driver's side tyre was out of round. Installed the two new tyres and a test drive on the fwy, smooth as you like! Spoke to my alignment guy and told him the problem was solved. He told me that had I told him the whole car shook, he would have told me to check the rears. He's my go to guy the next time. He was correct in his diagnosis! Anyone need alignment in LA, he is Andy's Alignment on Palmer in Glendale. He's the best!