Elastic shape optimization is a well-studied field with lots of results since the 1960s on the minimum possible compliance (describing the structural rigidity) for a given material volume and on the corresponding optimal microstructures. It is of interest not only for material design, but also for getting some understanding of structures appearing in nature, e.g. the microstructure of bones. Since associated solutions in general lead to non-natural, infinitely fine microstructure, there must be some additional complexity-limiting mechanism involved. One possible modification of the problem is to introduce a singular perturbation by adding the structure perimeter to the cost. For a uniaxial and a shear load in two space dimensions, corresponding results in terms of concrete geometric constructions fulfilling so-called energy scaling laws are already known. In my talk I will address the recently studied case of a uniaxial load in three space dimensions, show explicit microstructures and motivate how upper and lower bounds for their energy scaling laws were derived.