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Abstract For all altimeter missions, precise estimates of geophysical parameters are obtained thanks to an algorithm called "retracking" that fits an analytical model to the measured waveforms. The Brown model provides a good representation of the return echo over deep ocean surfaces and is commonly used. Many different chains can be considered (and have already been tested) for this processing. An unweighted Least Square Estimate derived from a Maximum Likelihood Estimator (MLE) (CitationDumont 1985; CitationRodriguez 1988) is implemented in most altimeter ground processing approaches (TOPEX, Jason-1, Jason-2, and Envisat). The aim of this paper is to evaluate the performance of two retracking algorithms based on the same least square principle: The MLE3 algorithm estimates three parameters (range, significant wave height, and power) whereas the MLE4 estimates four parameters (the three previous ones and the slope of the waveform trailing edge). MLE3 was used on Jason-1 before star tracker problems occurred. The MLE4 algorithm has been used for Jason-1 Version B products and onward and for Jason-2 products from the start of the mission. Both algorithms are compared in the paper. Advantages and drawbacks of both algorithms are pointed out showing notable benefits provided by MLE4 especially for waveforms that do not conform to the Brown model. Keywords: Radar altimetryretrackingwaveformssigma bloom event Acknowledgments This work was supported by CNES in the frame of the SLOOP project. Studies done for many years at CLS in the frame of the CNES SALP project have also greatly contributed to the general understanding of the waveform processing. We would like to warmly thank the two reviewers of this paper who have done very precise and constructive comments and suggestions. A great thank to reviewer Walter Smith, who made extremely interesting and relevant remarks. We would like to thank the CAL/VAL team at CLS and especially Y. Faugère and J.F. Legeais for providing us with some of their internal methods and expertise in altimeter data analysis.