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Seeking to explore the role of the order of lamination on the energy scaling for nucleation processes, we provide scaling laws for various model problems in two and three dimensions. In particular, we discuss (optimal) scaling results in the volume and the singular perturbation parameter for settings in which the surrounding parent phase is in the first-, the second- and the third-order lamination convex hull of the wells of the nucleating phase. Furthermore, we provide a corresponding result for the setting of an infinite order laminate which arises in the context of the Tartar square. 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