In this letter we address the classic problem of estimating the frequencies of multiple sinusoids in the presence of noise. We use line spectral frequencies (LSFs) and introduce the idea of 'closeness of LSFs' and propose two methods based on it. The minimum phase annihilating filter A(z) is estimated using MUSIC. The corresponding LSFs are then processed to estimate the frequencies, as opposed to estimating them from the roots that are closest to the unit circle. The closeness of LSFs criterion leads to a lower threshold when compared to MUSIC, with improvements ranging from 0 to 2 dB for the well-known two-sinusoids example; with pseudo-noise resampling the improvement is up to 4 dB. When applied to direction of arrival estimation, for the example considered by Shaghaghi and Vorobyov, the threshold improves by 6 dB and matches that given by the stochastic ML method. © 1994-2012 IEEE.