Low profile tires, also known as high performance or ultra high performance, are generally not ideal if you're looking for a smooth ride. They're most popular among drivers looking for superior handling and response, often people who do a little racing on the weekends.
A couple options for a softer ride that will fit your car are the Goodyear Eagle ResponsEdge and the Michelin Primacy MXV4. The Michelins come with a bit higher of a price tag, but both are classified as grand touring all-season tires, and will offer a more cushy ride than your current tires.
〉 Answered on Mar 18th, 2008 by Denise Koeth, Managing Editor at Tire Review Magazine
The previous owner may have not rotated the tires when they owned it, the tires could have been rotated just before you purchased the vehicle. Tires should be rotated about every other oil change, if for a prolonged period of time they have NOT been rotated, tires can adopted a wear pattern. Sometimes the rough ride can smooth out if not too severe, or you can try a re-rotate and balance.