We derive core masses and chemical compositions for luminous low-excitation planetary nebulae in the Magellanic Clouds. They are all on horizontal (heating) evolutionary tracks with core masses that concentrate between 0.55 and 0.6 M., and have low He/H and N/O ratios as expected from the relation found by Kaler & Jacoby. The behavior of carbon with core mass in uncertain, but it seems consistent with the behavior of carbon stars. There is also a suggestion that C/O anticorrelates with N/O. Below 0.63 M., O/H correlates positively with core mass. In combination with Kaler & Jacoby, Dopita & Meatheringham, and Aller et al., we now have accurate core masses for 80 planetaries in the Magellanic Clouds. Of these, 33 are members of a bright sample, defined as the set of 50 that fall in the top 1.5 mag of the [O III] luminosity function. We find excellent agreement between the core mass distribution of this group and the prediction of Jacoby that [O III]-bright planetaries have a very narrow Gaussian high-mass cutoff. The distribution of core masses on the log L-log T plane is qualitatively consistent with theoretical evolutionary rates.