Recently, the field of International Relations has seen increased interest in international hierarchy, and also an upswing in the analytical study of imperial logics of rule. Nonetheless, existing structural models of empire focus on core-periphery dynamics, and so cannot explain polities that display elements of both core and periphery. Therefore, I offer the new concept of ‘semi-cores’. Semi-cores are a specific form of historical political associations whereby certain imperial provinces are different from the others in terms of the close relationships it maintains with the imperial metropolis. Semi-cores are different by virtue of being relatively similar. The conceptualisation of semi-cores is followed by a section illustrating its logic, examining the relatively unfamiliar cases of Scotland and Norway and their position within the Danish and British empires, respectively. Although being separate imperial provinces, these were tightly connected to an imperial core. This concept helps us better understand imperial logics, and in the process shows how cultural factors can be formalised into accounts of structural logics of rule, impacting our understanding of both historical and contemporary hierarchical international affairs.