[1] In the paper "High-resolution analysis of the gravest seismic normal modes after the 2004 Mw = 9 Sumatra earthquake using superconducting gravimeter data" by S. Rosat et al. (Geophysical Research Letters, 32, L13304, doi:10.1029/2005GL023128, 2005), a method proposed by Dahlen [1982] was employed to compute the errors on the estimated frequencies; however, a mistake was made when implementing the method, so that the error bars were inconsistent with the signal-to-noise ratio. Indeed we used only one sample to estimate the noise spectrum instead of averaging over many samples of the demoded spectrum in the vicinity of the mode frequency. Another problem came from the fact that the estimated amplitude and quality factor of the mode used in the variance computation are correlated. We have then improved the least-squares fit by optimizingwith a Levenberg-Marquardt algorithm [Marquardt, 1963]. [2] To bring some constraints on the 3D density structure of the Earth, a reliable error estimate of the eigenfrequency is required [Häfner and Widmer-Schnidrig, 2012]. The revised error bars (Tables 1, 2 and 3) are much more robust than those published in the 2005 paper.