In the present study we perform direct numerical simulations (DNSs) of fully-developed turbulent square ducts with round corners at Reτ,c ∼ 180 and 360, and rectangular ducts of width-toheight ratios of 3 and 5 with rounded side walls at Reτ,c ∼ 180. The friction Reynolds number Reτ,c is based on the centerplane friction velocity and the half-height of the duct. The results are compared with the corresponding duct cases with 90° corners. We focus on the influence of the rounding on the mean cross-stream secondary flow and on further characterizing the mechanisms that produce it. Unexpectedly, the rounded ducts exhibit higher cross-flow rates and their secondary vortices relocate near the transition point between the straight and curved walls. This behavior is associated to the statistically preferential arrangement of sweeping events entering through the curved wall, which trigger an ejection on the adjacent straight wall. We have yet to find effective modifications to the corners or transverse ends of a rectangular duct that would render better rigorous modeling of two-dimensional channel flows.