Linear-Prediction-based (LP) methods for fitting multiple-sinusoid signal models to observed data, such as the forward-backward (FBLP) method of Nuttall (5) and Ulrych and Clayton (6), are very ill-conditioned. The locations of estimated spectral peaks can be greatly affected by a small amount of additive noise. LP estimation of frequencies can be greatly improved by singular value decomposition of the LP data matrix. The improved performance of the resulting new technique, which we called the principal eigenvector method (13, 14) is demonstrated by using it on one and two dimensional data.