Molecular dynamics (MD) investigations of the freezing of supercooled liquids can identify nuclei far smaller than can be detected in laboratory experiments, to date, and consequently can provide information about nucleation so far inaccessible to experiment. In a recent MD study of the freezing of clusters of SeF6, a new method of recording nucleation events was introduced. It involved the observation of times of first appearance of nuclei of the size of n. An advantage of the new approach is that it provides information about the size of the critical nucleus. For nuclei smaller than the critical size, it also avoids the overshoots of nucleation rates that precluded the application of the Miloshev-Wu method in the subcritical region. Kinetic information in the transient regime can be characterized by three parameters, the time lag, the reduced moment, and the steady state nucleation rate. To get some idea of how general the new approach is, a very different system was investigated, that of clusters of NaCl. Two different fitting functions were used to analyze the results. The first one adopted the log-normal probability distribution of Wu. The second function was a modification of Shneidman's analytical solution appropriate for large nuclei. The second function gave a rather good account of MD data for all nuclear sizes and temperatures and gave more stable results in the subcritical region. Several inferences of the sizes of critical nuclei were made. Applying the criterion for n* based on the Zeldovich solution of the Becker-Doring equations, we estimated the critical nucleus sizes to be 14, 18, and 24 ions for quench temperatures of 640, 690, and 740 K, respectively. Even though the interionic interactions initiating nucleation in salt are very different from the van der Waals interactions in clusters of SeF6, the characteristic aspects of the transient regimes of the two systems were quite similar.