Molecules with Hund’s rule violations between low-lying singlet and triplet states may enable a new generation of fluorescent emitters. However, only a few classes of molecules are known with this property at the current time. Here, we use a high-throughput screening algorithm of the FORMED database to uncover a class of compounds where the first excited state violates Hund’s rule. We examine this class of bridged [10]- and [14]annulene perimeters with saturated bridges, and relate them to known conjugated polycyclic systems with Hund’s rule violations. Despite the structural similarities with the related class of non-alternant polycyclic hydrocarbons, the mechanism is different in these bridged annulene perimeters. Here, two molecular orbital configurations contribute to each excited state. Consequently, a Hund’s rule violation can only be unambiguously assigned based on the symmetry of the lowest excited singlet and triplet states. With several examples of synthetically realistic molecules, the class of bridged [10]- and [14]annulenes thus provides a structural link between the known non-alternant and alternant (azaphenalene) classes of molecules violating Hund’s rule, and may open avenues for design of molecules with inverted singlet-triplet gaps.