Abstract More than a decade ago we published a calculation of nuclear ground-state masses and deformations in Atomic Data and Nuclear Data Tables [P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59 (1995) 185]. In this study, triaxial nuclear shapes were not considered. We have now enhanced our model and studied the influence of triaxial shape degrees of freedom on the nuclear ground-state potential-energy (mass) and ground-state shape. It turns out that a few hundred nuclei are affected to a varying degree with the largest effect, about 0.7 MeV, occurring near 108Ru. We provide here a table of the calculated effects of triaxial shape degrees of freedom. Although axial-asymmetry effects were not considered in the 1995 mass calculation, it did study the effects of reflection-asymmetric shape degrees of freedom ( ϵ 3 ) on nuclear masses. However, the magnitude of the effect was not tabulated. Here, we provide such a table. In addition we calculate the effect in a much improved fashion: we search a four-dimensional deformation space ( ϵ 2 , ϵ 3 , ϵ 4 , and ϵ 6 ). This is now possible because the computational resources available to us today are more than 100,000 times better than at the time we calculated the mass table published in 1995.