Burnt Copper Bottom Pots Heat Unevenly?

I have a set of copper bottomed stainless steel saucepans. A couple of which have had accidents over the years when the contents were burnt thanks to my lack of attention. This has created "hot spots" on the base wherein the contents can get burnt on despite my stirring them and watching the temperature. Is there any magic way of ridding myself of this persisent problem?

By dave Le frame