I had a weird story:

I had everything OK till my tires got too old. I had SS 225/70/R15 GENERAL 2000XP all four. I replaced two rear ones with 245/50R15 Kelly Charger. The car became VERY UNSTABLE. Felt like all the the tire are underinflated. Tried all the possible pressures. Nothing helped. So I got rid of the tires and bought Cooper Cobra 225/70/15. Handling got much better. So I thought that the problem is solved. But after a wile I realized that the car is still unstable at speed above 50 mph/: needs constant correction, especially when the road is not ideal.
I took the car to the alignment shop. They said that the alignment is ideal. I checked all the suspension - OK.
So finally I switched tires: Cooper on front General on rear and I COULD NOT RECOGNIZE MY CAR. It changed everything. Steering is fine.

Nobody could explain this phenomenon to me.