I have had nothing but glass top stoves for 35 years. I have used several different pressure cookers on them and every kind of pot or pan, flat bottom or not. I also have my pressing board on my wine room stove sometimes (yes, we make wine, too, which requires heating large quantities (10 pounds) of sugar in a gallon or less of water). I started with a white Corning top which discolored with heat and when it was replaced got a black top. Moved to a house with a 7 year old stove (now in the wine making kitchen) and bought a new stove for the family kitchen. I have had only the discoloration problem with the white cooktop but no problems of any sort with any type of pan. You have to use your own judgement but I wouldn't hesitate to do any type of cooking, canning or even pressing with my iron on a towel or pressing mat on the stove top. Good Luck with whatever you decide to do. (PS the stove salesman slammed an iron skillet down hard on the store stove top with no damage)