The performance of Reynolds Stress Transport (RST) models in non-equilibrium flows is limited by the lack of information about two dynamically important effects: the role of energy-containing turbulence structure (dimensionality) and the breaking of reflectional symmetry due to strong mean or frame rotation. Both effects are fundamentally nonlocal in nature and this explains why it has been difficult to include them in one-point closures like RST models. Information about the energy-containing structure is necessary if turbulence models are to reflect differences in dynamic behavior associated with structures of different dimensionality (nearly isotropic turbulence vs. turbulence with strongly organized two-dimensional structures). Information about the breaking of reflectional symmetry is important whenever mean rotation is dynamically important (flow through axisymmetric diffuser or nozzle with swirl, flow through turbomachinery, etc.). Here we present a new one-point model that incorporates the needed structure information, and show a selection of results for homogeneous and inhomogeneous flows.