The problem of estimating sinusoidal parameters of multiple sinusoids arises in many fields such as radar, wireless communication etc. Fourier based methods for frequency estimation are inadequate in the case of short data records with closely spaced sinusoids. Maximum Likelihood (ML) method is the best performing method so far, but it is the most computationally burdensome method. High resolution methods such as ESPRIT, MUSIC are popular due to their computational simplicity in the case of short data records. But these methods perform inferior to ML at low SNR. We propose methods based on Line Spectral Pairs (LSPs) for frequency estimation. Our proposed 2p method, which is based on LSP, achieves ML performance with significantly lower computational complexity (when compared to ML). We propose a threshold estimation-based switching criterion for switching to methods like ESPRIT for reducing computation at high SNR. Further, we propose a method that uses i) zero-padding and ii) removal-reestimation. This method outperforms ML, which is a new result and significant.