The 1.58 micron region is an atmospheric window in spectra of Titan. However, it has been known for a long time that numerous very weak absorptions of methane are present in that range that cannot be neglected (e.g. de Bergh et al. Astrophys. J., 311, 501, 1986; 329, 951, 1988). Their knowledge is very important for both atmospheric and surface studies of the satellite. We have undertaken at the Laboratoire de Spectrométrie Physique in Grenoble a study of these absorptions at very high sensitivity and low temperature (80 K) by CW-Cavity Ring Down spectroscopy. More than 15000 lines have had their intensities measured in the range 6150-6750 cm-1, and low energy values have been derived allowing to predict the temperature dependence of the absorptions in the region (work still in progress). Bands of CH3D are present in that range. They have been studied separately at USTC (Hefei-China) at room temperature by FTS spectroscopy and the contribution of the CH3D isotopologue to the absorptions observed in the laboratory spectra of methane obtained in Grenoble has been carefully evaluated. We will briefly describe the especially designed experimental set-up and the method used to an-alyze the spectra and obtain the line list at 80 K. We will then discuss the planetary applications that are foreseen. The obtained data will be very useful to get more accurate measurements of the D/H ratio in the atmosphere of Titan (as well as Uranus and Neptune), and to search for other minor constituents, from high-resolution planetary spectra. It will also be used to mea-sure spatial variations of methane in the low atmosphere of Titan from high spectral and spatial resolution observations. In addition, the DISR/Huygens Titan spectra will be re-interpreted by combining this new set of data with other data that have just been obtained on both sides of the window (Wang et al., in press; Sciamma-O'Brien et al., JQSRT, 110, 951963, 2009; Campargue et al., in press) to obtain more information on Titan's atmosphere and surface. Furthermore, these new laboratory data will help to eliminate the contribution of the atmo-sphere in Cassini/VIMS spectra of Titan, with the goal to derive the surface albedo at these wavelengths, and therefore get information on the surface composition. This work is part of a large effort concerning methane spectroscopy for Titan led by four French teams with the support of Agence Nationale de la Recherche .