You said that the converter was smoking, did you see if rattles, like something broken inside? What I think is happening is that the converter is letting some exhaust through but clogging up when you try to speed up. When you hit the gas the car shake, that is because you are putting fuel in the engine and the converter is not letting it go through, bogging down the engine. I would have the converter checked out. If you are driving at night and when you shut down the engine look to see if the converter is glowing red, that is a sign that the converter is clogged up.
Wednesday, February 18th, 2009 AT 3:19 PM