I didn't see this elsewhere on the forum or in a quick web search, so I thought I'd mention it. If you have a direct flight to the US from FCO you don't go to the usual screening area, there's a separate one for these flights.
We were recently flying back to the US from FCO and our tickets listed a gate in terminal E. We dutifully followed the signs to screening, the last one saying in big letters "A-E". However when we put our tickets on the scanner to open the gate it to enter the screening area it said something like "wrong area". A staffer near the gate said "direct US flight?" When we said yes, she said it was at the other end of the hall maybe 150 yards away. We had been reading the signage on the way in and nowhere did it indicate there was a separate area for these flights. In fact its only listed on a single sign on that far wall that you need to be within 25 yards to read. Asking around when seated and waiting for the flight, people said they were told of this entry when they checked bags. If you just do carry-on then you'll miss this advice.