I can't claim any brilliance here. This car was new to me and I had it at the shop to check a few things out. As soon as the tech started the car and shut it down a moment later he knew it needed new mounts. He described them as "collapsed". If you search on the subject of motor mounts you can find lots of info.
I posted on this before - but it was a classic case of "Holy Schnikes! So THAT is how it's supposed to be!!!" I just thought diesels idled very roughly and shut down by shaking the car hard a couple times.
When I picked the car up at the shop and started it I could not believe the difference. It was a totally different, fantastic feeling. I was grinning all the way home.
This job is not that expensive, even if you have a shop do it. If your car has some miles on it, it's probably worth it, IMHO.
smooth '95 E300D