τ envelope (τ total minus τ interstellar) values of stars in Messineo et al. (2018) are plotted versus the dereddened (K_s−W4)_o colours. Top panel: dusty models with a blackbody of 3200 K. Bottom panel shows dusty models of giant synthetic spectra with T_eff of 2600 K (in orange) and 3200 K (in green), log = 1, and Z = 0 dex, from the NextGen library of Hauschildt et al. (1999). For every synthetic spectrum, three different curves obtained with DUSTY are over-plotted. The dashed-dotted model shows dust grains with a fixed size of 0.1 μm. The dotted model uses the MNR distribution with a minimum of 0.005 um and a maximum of 0.25 μm. The dashed model is based on the MNR distribution and has a maximum of 0.1 μm.