This report presents a comparison of the relative capabilities of isolated three-component seismometers and small arrays for ascertaining the back-azimuth of regional events. The Cramer-Rao bound, a method well-known in estimation theory, is used to obtain quantitative predictions of the errors to be expected in estimating direction in the presence of noise. These quantitative error estimates form the basis for comparison. The theoretical approach taken assumes spatially coherent signals and incoherent noise. There are ranges of inter-station separation for which these models are reasonable approximations. Within the limitations on array aperture and element density imposed by the spatial correlation lengths of real signals and noise, the theory demonstrates that arrays have a definite advantage over isolated triaxial seismometers in estimating the direction of P waves. The gain in performance is proportional to the product of the aperture and the square root of the number of array elements. The performance of arrays of three-component elements in estimating P wave direction is examined also. Although such arrays have an advantage over arrays of vertical sensors for this purpose, the advantage is slight compared to the increased data bandwidth required. Consequently, the usefulness of horizontal sensors appears to depend on the importance ofmore » horizontally polarized phases for monitoring purposes or on the degree of noise polarization. Conditions of highly polarized noise favor the use of triaxial elements, since such noise can be reduced by polarization filtering.« less