Samples of zone-refined lead containing various amounts of silver as solute were solidified under well-controlled conditions to study the transition from cellular to dendritic freezing as a function of composition, speed of freezing, temperature gradient in the melt during freezing, and crystallographic orientation of the solidifying crystal. A comparison of the results of this investigation with those of Tiller and Rutter (1956) on alloys of tin in lead shows that to a first approximation the onset of dendritic freezing under any given growth conditions occurs at a critical value of the average solute concentration in the liquid at the solid–liquid interface, independent of whether the solute present is tin or silver.