A method is described for assessing the precision of wavefront direction-of-arrival (DOA) estimates made by acoustic arrays. Arrays operating in turbulent atmospheric boundary layers are considered. The method involves calculating the Cramer–Rao lower bound, which describes the best obtainable DOA precision (performance) for a given array and environment. For simplicity, it is assumed that the source is monochromatic, and multipath effects are not considered. The predicted performance bounds are found to degrade with increasing propagation distance, increasing frequency, and increasing turbulence strength. Performance predictions using several different three-dimensional turbulence models are compared: isotropic and anisotropic Gaussian models, the von Kármán model, and the Kolmogorov model, with the last in both intermittent and nonintermittent forms. When array performance is limited by turbulence (as opposed to background noise), the turbulence model strongly affects the calculated performance bounds. The results also suggest that degradation in DOA estimates results primarily from shear-generated, small-scale fluctuations in the wind velocity. Large, boundary-layer-scale eddies may still play a significant indirect role by driving intermittent episodes of high wind shear.