2002 Sable transmission shifting at high speed
My 2002 sable is acting oddly. When cruising at highway speeds, 65-75 mph, and needing to push the gas pedal more, to pass or go up a hill, the transmission seems to slip. Not slip exactly. But it will shift from 4th down to 3rd, and the rpm's rise, as expected when you try to accelerate. But then in the midst of accelerating, or maintaining speed uphill, the transmission will shift back into 4th gear, hesitate, and shift back to 3rd gear, then to 4th, then to 3rd. This goes back and forth until you let up on the accelerator. This does not seem like a natural shift point at all, and the car shudders when it happens. The car is driveable around town, and on the highway it works as long as you're content never passing anyone or maintaining speed uphill.
What do you think is going on and how can I fix it. Oh, transmission fluid looks good, level and color are fine.