Erratic shifting 2004 Deville DTS
 

I just recently acquired a 56,000 mile 2004 DTS. It seems to be constantly shifting at speeds in the 30's. As I hold the pedal constant, say at 35mph, the RPM drops to about 800, then jumps to 1,900 just to hold the speed. The pattern is continuous. Also, when I let up on the throttle, sometimes the car speeds up before slowing down.


There are no codes and the throttle body has been thoroughly cleaned out.


Any ideas as to what I need to look for?