Private jet travel promises luxury, but hidden costs, pricing complexity and poor service tell a different story. Here's how one company is changing that.

American Airlines is re-entering the private jet market nearly 30 years after selling its interest in fractional operator Flexjet and FBO chain AMR Combs.

Well-heeled travelers are paying more to fly private — even on previously booked flights — as fuel prices push $4.65 a gallon on average. While private jet passengers typically have deep pockets, some ...