We have investigated a wide range of structures containing InAs and In 0 . 5 Ga 0 . 5 As self-organised quantum dots grown on (100), (311)A and (311)B GaAs substrates. The photoluminescence line width for quantum dots grown on the high-index planes is significantly narrower than those typically observed for (100) quantum dots. Bright room temperature electroluminescence is observed from a p-i-n device with the intrinsic region containing In 0 . 5 Ga 0 . 5 As quantum dots grown at the (311)B orientation. Photoluminescence spectra were measured in magnetic fields up to 43T for both quantum dot and wetting layer samples. From the diamagnetic shift of the photoluminescence lines, we have estimated the spatial extent of the carrier wave functions and compare these with the geometrical dot size obtained from microscopic investigations. This comparison suggests a qualitative model to explain the narrow photoluminescence of the quantum dots grown on (311)A and B planes.