There are several different types of automatic gearboxes around. The traditional three speed planet gear type are more suited to large engines. Most commonly they are paired with torque converter clutch. This torque converter coupled with only three gears makes very hard going for a small engine.

A consortium of car manufactures developed an idea that came from DAF of the continuously variable gearbox. If memory servers it was Ford, Fiat, Nissan and Citroen. This gearbox is much better suited for small cars as it doesn't have the torque converter and but dose have an infinite number of gears. Have a look for a Ford Festa, Fiat Punto, Nissan Micra or Citroen's Saxo, C2, C3. These will be both fuel efficient and nippy.