Over the past 15 years, our knowledge of the interior of the Sun has tremendously progressed by the use of helioseismic measurements. However, to go further in our understanding of the solar core, we need to measure gravity (g) modes. Thanks to the high quality of the Doppler-velocity signal measured by GOLF/SoHO, it has been possible to unveil the signature of the asymptotic properties of the solar g modes, thus obtaining a hint of the rotation rate in the core (García et al. 2007, 2008a). However, the quest for the detection of individual g modes is not yet over. In this work, we apply the latest theoretical developments to guide our research using GOLF velocity time series. In contrary to what was thought till now, we are maybe starting to identify individual low-frequency g modes. . .