A 32 x 32 microelectromechanical systems deformable mirror is controlled in closed loop with a spatially filtered Shack-Hartmann wavefront sensor and a Fourier-transform wavefront reconstruction algorithm. A phase plate based on atmospheric turbulence statistics is used to generate a 1 microm peak-valley static phase aberration. Far-field images and direct phase measurements of the residual are used to compare performance with and without the spatial filter. Use of the spatial filter reduces error in the controllable band from 20 to 6 nm rms. Residual phase power is reduced by more than a factor of 5 for all spatial frequencies up to 0.85 x 1/2d, with a maximum attenuation factor of 37.