We attempt to improve accuracy in the high-wavenumber region in DNS of incompressible wall turbulence such as found in fully developed turbulent channel flow. In particular, it is shown that the improvement of accuracy of viscous terms in the Navier–Stokes equations leads to the improvement of accuracy of higher-order statistics and various spectra. It is emphasized that increase in required computational cost will not be crucial when incompressible flow is simulated, because the introduction of a higher-order scheme into the viscous terms does not increase computational cost for solving the Poisson equation. We introduced fourth-order and eighth-order central compact schemes for discretizing the viscous terms in DNS of a fully developed turbulent channel flow. The results are compared with those using second-order and fourth-order central-difference schemes applied to the viscous terms and those obtained by the spectral method. The results show that accuracy improvement of the viscous terms improve accuracy of higher-order statistics (i.e., skewness and flatness factors of streamwise velocity fluctuation) and various spectra of velocity and pressure fluctuations in the high-wavenumber region. Copyright © 2013 John Wiley & Sons, Ltd.