We discuss the image improvement from an adaptive optics system that selectively corrects for phase perturbations with large angular coherence lengths. Selecting phase perturbations with large angular coherence lengths effectively sets the correction to turbulence of all spatial frequencies at the ground and to turbulence of progressively lower spatial frequencies at higher altitudes. The performance of a high-order curvature system (85 elements) on a small telescope (4 meters) across a field of view of roughly six arcminutes diameter is simulated using Monte Carlo simulations. The implementation studied assumes a single correcting element conjugate to the ground with multiple wave front sensors each pointed at a different star within the field of view. The image full-width at half maximum (FWHM) is reduced by up to a factor of two over the uncorrected case. Even though the number of guide stars is large (n~3), the sky coverage is similar to that for a classical adaptive optics system since the acquisition field is much larger (~35 square arcminutes). In principle the approach could be extended to multiple laser guide stars and larger apertures. The requirements for the laser are relaxed since the sampling of turbulence is preferentially at low-altitudes (e.g. Rayleigh beacons).