I don't think it'd be good to install directly on your old tops. For 1 is the Corian just sheet material or is it an actual countertop ? Then you have the edge issue to deal with & the backsplash. Is your current laminate backsplash formed to the top or seperate ? Also there's the thickness issue you would get into with the sink & faucet cutout, probably wouldn't work, especially with the faucet. It's best to remove old countertops & start with a clean new surface to adhere corian to, if it's only sheet goods.