Fast-Fourier-transform-based simulations of single-layer atmospheric von Kármán phase screens and Kolmogorov scintillation screens up to hundreds of meters in size were implemented and tested for applications with percent range accuracy. The tests included the expected and the observed structure and pupil variance functions; for the phase, the tests also included the Fried turbulence parameter r0 measured by the seeing and by a simulated differential image motion monitor. The standard compensations used to correct the undersampling at low spatial frequencies were improved, and those needed for the high spatial frequencies were determined analytically. The limiting ratios of the screen sampling step to r0 and of the screen size to the pupil aperture were estimated by means of the simulated data. Sample results are shown that demonstrate the performances of the simulations for single-layer Kolmogorov and von Kármán phase screens up to 200 m in size and for Kolmogorov scintillation screens for pupils up to 50 m of aperture.