© 2018 American Physical Society.In this study, we present a statistical analysis of the level structures of four highly charged actinide ions: Bk xii, Cf xii, No xiii, and Md xiv. In these ions, 5f wave-function contraction gives rise to a manifold of levels arising from configurations with partially filled 5f and 6p subshells. The cumulative effects of configuration interaction (CI) between these configurations results in a complete breakdown of the independent particle model used in the labeling of the states and leads to the formation of so-called "compound" states. Properties of the calculated level structures have been analyzed using the techniques of random-matrix theory (RMT). Standard statistical measures, such as the repulsion parameter q, the covariance of adjacent spacings cov(si,si+1), and the Dyson-Mehta statistic Δ3(L), have been computed for specific Jπ interacting sets belonging to the four aforementioned ion stages. In the majority of cases, these calculations are found to be in very good agreement with the RMT-predicted values for these quantities. This study therefore extends previous identifications of RMT-like level fluctuations in the level spectra of lanthanide ions to high-Z, moderately charged actinide ions.