The notion of a ‘homogeneity of style’ in the historiography of military architecture carries the risk that those forms that are not directly traceable in modern historiography are too easily dismissed as out of bound or simply as the results of external factors. This article is about fortifications that stand out because the walls between the bastions are not straight but concave. An essay by Renty and Philippeville about structures along the Habsburg-French border and the Portuguese overseas fortifications at Mazagão in Morocco and the São Sebastião fortress in Mozambique demonstrates that this is a recurring element in the ground plans of various sixteenth-century strongholds. The external factors to which this phenomenon has sometimes been ascribed are not convincing in any of these cases, which is why the need for a theoretical foundation arose. An analysis of contemporary treatises on architecture reveals that the concept was discussed and even propagated as an ideal defense system by various theorists, in different variations. Niccolò Tartaglia appears to have been the first author who wrote about the idea of providing covering fire from both the bastions and from inward bending walls. In his treatise Quesiti et inventioni diverse, first published in Venice in 1546, he criticized the traditional square ground plan of fortresses because, in his view, it did not offer the ideal cover and was too vulnerable. The two publications that most extensively discussed alternative concepts were the works by Jacomo Fusto Castriotto Galasso and Alghisi da Carpi, which were published in 1564 and 1570, respectively. Using concave curtain walls can be understood as an attempt to combine the advantages of the tenaille and bastion systems. In particular around the middle of the sixteenth century, when assailants would aim their cannon fire more at the bastions instead of at the well-covered curtain walls, the need for extra cover for the faces arose. Whereas Alghisi’s work remained highly theoretical, Castriotto’s ...