any suggestions for cheap flights to Italy on very short notice

ok so I have the chance to maybe do a fun thing IF I can get to Rome cheap enough in about 3-1/2 weeks..

Checking all my usual haunts and the airfares are very high due to high season and also less than 30 days booking..

Does anyone have any secrets or suggestions they can share for looking for a freakishly cheap deal at the absolute worst time of the year on short notice?

I know it's a tall order!!!!