Control of as-cast grain size is important for aluminium alloys and is achieved by inoculation. The usual analysis of grain refining (based on recalescence in small test samples) is not applicable for larger melts showing directional solidification. For the latter case, the factors controlling grain-refining efficiency (the fraction of inoculant particles initiating grains) are explored. It is suggested that the major factor limiting the efficiency is impingement of growing grains on inoculant particles. Predictions are made for the variation of grain size with refiner addition level, solute content in the melt and cooling rate. The grain size is predicted to be independent of solidification velocity or thermal gradient at a given cooling rate. The analysis is also applied to the columnar-to-equiaxed transition; there is no characteristic equiaxed grain size associated with this transition.