Some high class quiet compound :
- Al Jazi (most of them Exon employee)
- Al Fardan (maersk and shell)
- Al Bustan Compound (just behind ramada hotel)
- Al Naseem Garden (behind ponderosa)
- Green Village compound ( just next door to Hyatt Plaza and Villagio)
- City Garden 1 and 2 (just next to Airport Road).

There are loads compound in Doha, but i have no idea which area your preference.