Two approaches--one parametric and one non-parametric--to the source bearing estimation problem for narrowband passive sonar are presented. The parametric technique does not directly involve estimation of a spatial spectrum. Rather, an optimization problem is solved for a set of parameters (such as signal strengths and directions of propagation, noise strength, and inter-signal coherences) which minimizes the norm of the error between the parametrically expressed true correlation matrix and the estimated correlation matrix. Simulations suggest that this method is capable of resolving completely coherent sources separated by much less than a beamwidth at low (0 dB) signal to noise ratios. A competing non-parametric method uses spatial averaging to estimate spatial correlation matrices more accurately. Spatial averaging is shown to reduce inter-signal coherence. Two types of spatial averaging are discussed--subaperture averaging and redundancy averaging. Subaperture averaging is shown to increase the accuracy of the estimated correlation matrix and to reduce coherence without perturbing estimated source bearings. However, it is unable to noticeably reduce inter-signal coherence if the signals are closely spaced. Redundancy averaging is also shown to increase accuracy and reduce coherence and is more effective with closely spaced coherent signals than subaperture averaging. However, redundancy averaging may induce bias in estimated source locations if there are coherent sources. Our results indicate that the parametric method offers significantly improved performance over the more traditional methods. As spatial averaging is essentially a refinement of traditional methods, it is perhaps overshadowed by the parametric method. However, the parametric method requires further study to empirically determine its effectiveness and meanwhile, spatial averaging may be a fruitful way to reduce the negative effects of coherent signals on traditional bearing estimation methods.