Jordan’s Royal Aero Sports Club (t 079 730 0299, w royalaerosports.com), based at Aqaba airport, runs sightseeing flights over the Wadi Rum desert in ultralight aircraft (JD75 for 20min, JD200 for 1hr). They also offer a serene one-hour journey at dawn by hot-air balloon over the deserts of Wadi Rum (JD130 per person, minimum three people). All these must be booked in advance. Occasionally, the company brings in skydiving instructors from Dubai for tandem jumps from 10,000 feet above the sands: check the website for dates and details.
The Royal Jordanian Gliding Club (t 06 487 4587, w rjglidingclub.com), based at Marka airport in Amman (with additional sites in Aqaba and Rum), can take you up for a uniquely silent view of the capital (JD30). They also have ultralights and single-engine aircraft.