Some folks do run the iron over the ribs after shrinking and some don't, I'm a don't. I use Ultracote and when it shrinks it goes down tight and the heat from the heat gun glues the covering to the ribs pretty well. You don't know how well until you pull the covering to do repairs or recover. If you iron down on the ribs before you shrink it creats a problem sometimes like wrinkles or nasty looking spots in the covering. Makes a cool sounding pop when it does shrink tight though!