The out-coupling efficiency of organic light-emitting diodes (OLEDs) may be significantly increased by use of a low-index host material for the organic emitters. We report on modelling undertaken for substrate-emitting and top-emitting OLED structures and show that up to a 2.5 fold increase in out-coupling efficiency, over that for structures containing a standard emissive layer, may be achieved in both cases. The relationship between radiation efficiency and refractive index varies for each type of structure and this is discussed, as is the nature of the electromagnetic (EM) modes supported.