This paper presents a new state-space method for spectral estimation that performs decimation by any factor D while it imposes no constraints to the model order with respect to D. The new method, called DESED, as well as its Total Least Squares version called DESED-TLS, makes use of the full data set available and is based on SVD in order to estimate frequency, damping factor, amplitude and phase of exponential sinusoids. The new methods are tested in the ?eld of spectroscopy, where accuracy of parameter estimation is of utmost importance. They are compared against HTLS -an existing method for spectral estimation- its decimative version HTLSD and against a purely decimative method (CONDED). Monte-Carlo based experiments performed on a typical simulated NMR signal prove the new methods to be more robust, especially for low signal to noise ratio.