We simulate turbulence in a plane Couette geometry by a spectral method intermediate between full resolution and the complete elimination of small modes common in large eddy simulations. The wave number grid is sparse in spanwise and downstream direction, with a total number of modes proportional to Re(3/4) lnRe. At a Reynolds number of 2000 we could suppress more than 80% of the modes and still obtain a fairly accurate resolution of the boundary layer structures and friction factors. For a wide range of resolutions, the mean velocities are described by logarithmic profiles, with von Karman constant near a value of 0.4.