One of the key observations in the Princeton Superpipe was the late start of the logarithmic mean velocity overlap layer at a wall distance of the order of 10(3) inner units. Between y(+) approximate to 150, the start of the overlap layer in zero pressure gradient turbulent boundary layers, and y(+) approximate to 500, the Superpipe profile is modelled equally well by a power law or a log law with a larger slope than in the overlap layer. This paper demonstrates, that the asymptotic mean velocity profile in turbulent plane channel flow exhibits analogous characteristics, namely a rather sudden decrease of logarithmic slope (increase of.) at a y(+) of approximately 600, which marks the start of the actual overlap layer. The demonstration results from the first construction of the complete mean velocity inner and outer asymptotic expansions up to order O(Re-tau(-1)) from direct numerical simulations (DNS) at moderate Reynolds numbers. The O(Re-tau(-1)) contribution to the indicator function Xi(+) = y(+) (dU(+) /dy(+)) is found to be important and to prevent the direct determination of. from currently available channel DNS. A preliminary, leading-order analysis of a Couette flow DNS, on the other hand, yields an increase of logarithmic slope (decrease of kappa) at a y(break)(+) approximate to 400. The correlation between the sign of the slope change and the flow symmetry motivates the hypothesis that the breakpoint between the possibly universal short inner logarithmic region and the actual overlap log-law corresponds to the penetration depth of large-scale turbulent structures originating from the opposite wall.