A new procedure is introduced to determine the three principal parameters that characterize homogeneous nucleation, namely the "reduced moment," the time lag, and the steady-state rate. This information can be derived, in principle, by monitoring the spontaneous freezing occurring in molecular dynamics simulations of supercooled liquids. The new procedure has been applied to the set of 2500 nucleation events acquired in a prior investigation of the freezing of 2500 independent large molecular clusters of SeF6. In this procedure the times of the first appearance of nuclei containing n molecules is determined for each cluster, considering values of n ranging from small to very large. This procedure avoids the mixing together of a large distribution of nuclear sizes that resulted from our previous algorithm based on the times of onset of nucleation. Such a superposition of sizes appears to have seriously inflated the derived reduced moment parameter characterizing transient nucleation, thereby favoring the 1969 theory of Kashchiev over the more recent treatments of Wit and Shneidman. Results of the new procedure, as interpreted by a provisional mode of analysis, reverse the assessment of the theories and provide, as well, a new method for determining the size of the critical nucleus.