The graph-theoretical Hückel-London-Pople-McWeeny (HLPM) approach to π-electron ring-currents and bond-currents was recently applied to a newly defined series of hypothetical conjugated hydrocarbons called the p-coronenes (with p odd and p > 3) and that investigation ostensibly indicated that the first four of these structures conform to the annulene-within-an-annulene model [Dickens et al., Phys. Chem. Chem. Phys., 2013, 12, 8245]. However, more-refined calculations reported here, which are based on a more-realistic geometry and the ipso-centric ab initio formalism, contradict this finding and indicate that, so far, the only member of the p-coronene series that definitely obeys the AWA rule is its very first member, 5-coronene (also known as [10,5] coronene).