Conceptually, these annulenes are a bridge between the known alternant (cyclazine and derivatives) and non-alternant (e.g., isopyrene and pentalene derivatives) classes of Hund's rule violations, as they all possess double-bond delocalized π-conjugated perimeters. We discuss the structural traits of annulene perimeters in relation to their parent molecules, some of which themselves also exhibit Hund's rule violations. However, the mechanism of this class of annulene perimeters with a saturated bridge differs from known classes. Here, the excited state is always a linear combination of two excitations, typically involving transitions from the HOMO-1 and HOMO into the LUMO and LUMO+1, respectively. Nonetheless, the electron configuration (and thereby the Hund's rule violation) is straightforward to identify in most cases as the singlet and triplet states are the lowest lying excited states within their irreducible representation.