Here's a sale from an airline that doesn't put them out on the regular. Royal Jordanian is having a Super Saver Sale on flights from North America to its hub in Amman and then beyond to the Persian Gulf and Mediterranean.
Flights are valid from September 16 through March 15, 2019, with a purchase window for tickets through next week, July 12, 2018. Travel days will vary by route, but I had the most luck with Tuesday and Thursday departures. Flights departing Detroit are a little harder to find than the rest but they are out there on certain dates. The Royal Jordanian site does hiccup here and there but you should be able to find them with the flexible date search.
As for restrictions, there is a maximum stay of 45 days and a blackout period during Christmas and New Year.
These are some excellent deals to destinations that don't always get price cuts, especially to Aqaba, where you can dive the Red Sea and take a trip up to the modern world wonder - Petra.