A new state-space method for spectral estimation that performs decimation by factor two while it makes use of the full set of data available is presented in this paper. The proposed method, called DESE2, is based on Singular Value Decomposition in order to estimate frequency, damping factor, amplitude and phase of exponentially damped sinusoids in the presence of noise. The DESE2 method is compared against some previously proposed methods for spectral estimation that lie among the most promising methods in the field of spectroscopy, where accuracy of parameter estimation is of utmost importance. Experiments performed on a typical simulated NMR signal prove the new method to be more robust, especially for low signal to noise ratio. The new method outperforms the other two not only by presenting lower failure rates but also by incorporating enhanced discriminative analysis while at the same time it benefits from the use of the full data set.