Previous work covers building a tower from a stack of homogeneous rectangular plates, each with a maximum shift in displacement. We suggest using plates shaped as curvilinear triangles bounded by segments of power-law functions. The masses of the plates and the position of their center of mass are calculated and measured experimentally after cutting them out from cardboard and aluminum sheets. A computer simulation of the displacement towers is combined with their live building. Individual maximum shifts of the plates in the stack prove to be much bigger the higher the power coefficient of the boundary curves. The resulting total overhang of such a displacement tower may exceed that of a stack of traditionally used homogeneous rectangular cards.