The maximum likelihood (ML) method of estimating the frequencies of p sinusoids in the presence of AWGN is computationally very costly because of the dimensionality of the error surface; the advantage is that the ML method has the lowest threshold among all known practical estimators. We propose a low complexity method using Line Spectral Pairs (LSPs), where the LSPs are derived from an estimated A(z) obtained using Multiple Signal Classification (MUSIC) method. The proposed method evaluates the likelihood function at significantly fewer number of points-at most 5p C- p -for getting the estimates. Furthermore, no iterative finer search is required. Nevertheless, the proposed method's threshold is comparable to that of ML when tested using the well-known two-sinusoids example; similar performance was observed in the case of three sinusoids. Further improvements were observed when the beamformer function was used for detecting and removing outliers. For the two-sinusoid case, outlier removal resulted in a threshold that was lower than that of ML by as much as 9 dB (3π/2 case). We also present results for a direction of arrival (DOA) estimation example that results in the same threshold as that of ML. © 2019 IEEE.