We have studied the growth behaviour of sub-10 nm NaYF₄ upconversion nanocrystals of the hexagonal β-phase and the cubic α-phase. Ostwald-ripening of such particles in oleic acid/octadecene solvent results in broadening of the particle size distribution if the colloid contains particles of one crystal phase only. Narrow size distributions are formed only if β-phase particles grow in the presence of an excess of α-phase particles. Such binary mixtures of α-phase and β-phase particles form intrinsically when colloids of α-phase particles are heated for a sufficiently long time, because seeds of the β-phase nucleate in the solution after some time at high temperatures. Since the number of seeds determines the final size of the β-phase product, control of the nucleation is crucial for controlling the final particle size. We show that the number of β-phase seeds strongly depends on the composition of the α-phase known to form solid solutions Na₁-xYF₄-x in the range from x = 0 to x = 4/9. Sodium-deficient α-phase particles form a negligible number of β-phase seeds whereas α-phase particles with high sodium content yield a very large number of seeds. By taking advantage of this dependence and modifying the synthesis of the α-phase particles accordingly, small phase-pure β-NaYF₄:Yb,Er particles with a size smaller than 6 nm can be prepared in oleic acid/octadecene just as well as much larger particles.