The very small solder joints that now account for an increasing proportion of the connections on which modern electronics depends are typically made up of only a few grains, sometimes only a single grain. This combined with the high degree of anisotropy in the mechanical properties of the body-centred tetragonal beta-tin crystal is a significant factor in determining the response of the joint to the strain to which it is subject in service, with consequent implications for reliability. The superior reliability in joints with multiple small grains of random orientation suggests that it would be advantageous if the solder alloy could be made to solidify with that fine grain structure. In the study reported in this paper the effect of trace additions of selected elements on the grain structure of pure tin and lead-free solder alloys was observed. The elemental additions were chosen on the basis of previous research as well as an analysis of relevant binary phase diagrams. Solidification theory suggests that an objective of the addition should be to promote the rapid development of a constitutionally undercooled zone ahead of the advancing solid/liquid interface since this is known to favour the repeated nucleation required to achieve a fine grain structure. The results contribute to the growing body of knowledge on the development of microstructure in lead-free solder alloys.