Two approaches are considered in an attempt to mollify previous observations regarding the very negative impact that voter abstentions can have on Plurality Rule, Negative Plurality Rule and Borda Rule when voters' preferences are assumed to be statistically independent. The first option is to add a degree of dependence among voters' preferences, and the second is to consider extensions of these three voting rules by using each as the basis for a two-stage elimination election procedure. The end result in both cases is that improved results are indeed observed for both Condorcet Efficiency and the probability that a Borda Paradox is observed for larger values of voter participation rates. The very disturbing result is that both of these options actually tend to make things worse with voter participation rates of 40% or less, and voter participation rates are observed in practice at this level.