Master alloys based on the system Al-Ti-B are commonly used as grain-refining additives to aluminium castings. It has been shown in previous work that TiB2 particles are the most common heterogeneous nucleation sites for aluminium crystals. Additions of potent nucleating particles to an aluminium melt do not, however, cause grain refinement automatically; there must be a driving force for nucleation as well as subsequent growth. The driving force at slow cooling rates can be present in the form of constitutional undercooling caused by alloying elements that do not interact with each other or the nucleating particles. The influence of hypoeutectic concentrations of silicon and iron and hypoperitectic concentrations of titanium on the alpha-Al grain size has been studied. It is found by use of a two-thermocouple thermal analytical technique and from studies of the microstructure that the growth-restricting effect of Fe, Si and Ti are additive at low concentrations. The thermal analytical technique allows us to determine the point where the dendrites grow together forming a continuous network. The time lapse from nucleation to the point where the dendrites impinge on each other is used to calculate the average growth rate of the dendrites. The grain diameter is proportional to the dendrite growth rate, and once the equiaxed dendritic growth is completed, the final grain size is determined. A deterioration in the grain-refining effect occurs at high solute concentrations. Increasing solute concentrations decreases the dendrite tip radius, counteracting the solute effect. At high solute concentrations, the dendrite tip radius eventually decreases to a critical limit where capillary effects start to become important and the growth rate increases.