Sunspots are locations on the Sun where unique atmospheric conditions prevail. In particular, the very low temperatures found above sunspots allow the emission of H_2 lines. In this study we are interested in the radiation emitted by sunspots in the O VI lines at 1031.96 A and 1037.60 A. We use SOHO/SUMER observations of a sunspot performed in March 1999 and investigate the interaction between the O VI lines and a H_2 line at 1031.87 A found in the Werner band. The unique features of sunspots atmospheres may very well have important implications regarding the illumination of coronal O+5 ions in the low corona, affecting our interpretation of Doppler dimming diagnostics.