The accuracy of the Sea Surface Salinity (SSS) retrieved from L-Band radiometer measurements is strongly dependent on the reliability of the dielectric constant model. Two new parametrizations were recently developed based on one hand on the Soil Moisture and Ocean Salinity (SMOS) satellite multi-angular brightness temperature measurements by Boutin et al. (2021) (BV), and on the other hand on new George Washington University laboratory measurements by Zhou et al. (2021) (GW2020). These two approaches are fully independent. For most SSS and Sea Surface Temperature (SST) conditions commonly observed over the open ocean, the relative variations of brightness temperatures Tb simulated through the BV and GW2020 parametrizations agree particularly well, and better than with earlier parametrizations previously used in the SMOS, Soil Moisture Active Passive (SMAP) and Aquarius SSS retrievals. Nevertheless, uncertainty remains, especially below 10°C where a ~0.1K relative difference between the two models is observed. This motivates the development of a revised parameterization, BVZ, based on a methodology similar to that used to derive BV but using GW2020 instead of SMOS measurements. Compared to the GW2020 parameterization, BVZ is derived with a reduced number of degrees of freedom, it relies on TEOS10 PSS78 conductivity-salinity relationship and on previously derived static permittivity of fresh water. One month per season of SMOS data have been reprocessed in 2018 using BV, GW2020 and BVZ. We find the best overall agreement between SMOS SSS and Argo SSS with BVZ parametrization, with noticeable improvement in the 5°C-15°C SST range.