Context. Diffuse Stellar Bands (DIBs) are ubiquitous in stellar spectra. Traditionally, they have been studied through their extraction from hot (early-type) stars, because of their smooth continuum. In an era where there are several going-on or planned massive Galactic surveys using multi-object spectrographs, cool (late-type) stars constitute an appealing set of targets. However, from the technical point of view, the extraction of DIBs in their spectra is more challenging due to the complexity of the continuum. Aims. In this contribution we will provide the community with an improved set of stellar lines in the spectral regions associated to the strong DIBs at λ6196.0, λ6269.8, λ6283.8, and λ6379.3. These lines will allow for the creation of better stellar synthetic spectra, reproducing the background emission and a more accurate extraction of the magnitudes associated with a given DIB (e.g. equivalent width, radial velocity). Methods. The Sun and Arcturus were used as representative examples of dwarf and giant stars, respectively. A high quality spectrum for each of them was modeled using TURBOSPECTRUM and the VALD stellar line list. The oscillator strength log(g f ) and/or wavelength of specific lines were modified to create synthetic spectra where the residuals in both the Sun and Arcturus were minimized. Results. The TURBOSPECTRUM synthetic spectra based on the improved line lists reproduce the observed spectra for the Sun and Arcturus in the mentioned spectral ranges with greater accuracy. Residuals between the synthetic and observed spectra are always ∼ < 10%, much better than with previously existing options. The new line list has been tested with some characteristic spectra, from a variety of stars, including both giant and dwarf stars, and under different degrees of extinction. As it happened with the Sun and Arcturus residuals in the fits used to extract the DIB information are smaller when using synthetic spectra made with the updated line lists. Tables with the updated parameters are provided to the community.