The anomalous low-energy E2-related behavior of a triaxially deformed nuclei is examined within the framework of the interacting boson model. The results show striking features that include a B(E2; 4(1)(+) -> 2(1)(+))/B(E2; 2(1)(+) -> 0(1)(+)) < 1.0 transition rate and a E(4(1)(+))/E(2(1)(+)) > 2.0 excitation energy ratio that can be tracked back to a finite-Neffect, which in a large-Nlimit of the theory yields normal results for a stable gamma-deformation. This description is shown to explain experimentally observed results in Pt-172 and Os-168, and in doing so yields a deeper understanding of the physical features of a soft triaxially-deformed nucleus.