We study the bistability between a 180° twisted state and its topologically equivalent planar vertical state in pure nematics in the presence of a holding voltage. These bistable states can be distinguished optically by incorporating a pleochroic dye guest into the liquid crystal host. The holding voltage range ΔV of the bistability is found to increase with decreasing k1/k 3 and with decreasing dielectric anisotropy. With reasonable elastic constants and dielectric anisotropy parameter (ε∥ — ε ⊥)/ε⊥ = 0.05, the theoretical holding voltage range ΔV is about 7 % in the idealized case of perfect alignment and zero boundary tilt bias. With such boundary conditions, the cell would be subject to oppositely tilted and oppositely twisted domains, whose elimination would entail a drastic reduction of ΔV and some loss of contrast. While the bistability could probably be demonstrated experimentally, it is not likely to be practical in displays without major materials innovation to obtain significantly lower values of the elastic constant ratio k1/k3