We had tickets for 8:15 AM when the Uffizi opened. We planned our Uffizi strategy the night before -- create a prioty list of the rooms we want to see. Our strategy was to walk quickly (up two very, very long flights) to first the Botticelli room and have about 20 minutes of viewing in an empty room. Then as the room filled up with tourists we moved on to the next room on our list. Essentially we saw the Uffizi in "backwards" order to minimize the crowds.