Nucleation during solidification is heterogeneous in nature in an overwhelmingly large fraction of all solidification events. Yet, most often the identity of the heterogeneous nucleants that initiate nucleation remains a matter of speculation. In fact, a series of dedicated experiments needs to be designed in order to verify if nucleation of the material under study is based on one type of heterogeneous nucleant and if the potency of that nucleant is constant, e.g. for a population of individual droplets, or stays constant over time, e.g. throughout repeated melting/solidification cycles. In this work it is demonstrated that one way to circumvent ambiguities and analyze nucleation kinetics under well-defined conditions experimentally is given by performing statistically significant numbers of repeated single-droplet experiments. The application of proper statistics analyses based upon a non-homogeneous Poisson process is shown to yield nucleation rates that are independent of a specific nucleation model. Based upon this approach nucleation undercooling measurements on pure Au, Cu and Ni as model materials have confirmed that the experimental strategy and analysis method are valid. The results are comparable to those obtained by classical nucleation theory applied to experimental data that has been verified to comply with the assertions that are necessary for applying this model framework. However, the results reveal also other complex nucleant-sample interactions such as an initial transient undercooling behavior and impurity removal during repeated cycling treatments. The transient undercooling behavior has been analyzed by a nucleant refining model to provide new insight on the operation of melt fluxing treatments.