My STS4 now shifts like a cadillac is supposed to, and like the eight ones I have had before. No more engine surging, rpms bouncing, and indecision when shifting. I cannot express how much better the car drives now. It is night and day difference that the silly dealer could not recognize, I am the one who found and brought them the TSB below and FORCED them to do it.
Anyway Technical Service Bulletin #10017146 will fix your car. The official verbal description from the NHTSA is: TCC surge, shudder, chuggle on light load just after torque converter engagement. Hope this helps those of yoiu who have encountered the same problem.
MODERATOR NOTE: 3456D is the correct TSB number. -Jesda