It is shown for a representative set of isomeric benzenoids that pi-electron partitions and signatures can serve for characterizing and ordering benzenoids. Benzenoid signatures (sequences S-6 through S-1 where the subscripts correspond to numbers of pi electrons in all rings) are obtained by examining the numbers of assigned pi electrons ranging from 6 to 1 for each ring in all resonance structures. The pi-electron partitions and signatures of all 33 non-isoarithmic peri-condensed benzenoid hydrocarbons with eight rings and four contiguous internal carbon atoms allow an ordering of these benzenoids that agrees fairly well with increasing numbers of Kekule valence structures and Clar sextets. Interestingly, an excellent correlation (R-2 > 0.99) is observed between S-6 + S-5 + S-2 + S-1 and S-4 + S-3, and an explanation for this observation is provided: the number P of pi electrons is divided unequally between two components: S-34 S-4 + S-3 and S-1256 S-6 + S-5 + S-2 + S-1 so that S-1256 or the quotient S-1256/S-34 = Q can serve as a new metric for perfect matchings of polyhexes and a criterion for ordering and for evaluating the complexity of isomeric benzenoids quantitatively.