A study of IUE spectra of eight cool G4-K0 giants shows evidence of interstellar Mg II absorption in all the stars but Delta Dra. Sharp features are detected in the emission wings of four stars, while only strong asymmetries of the emission profiles are noted in three cases. In all the cases studied, the interstellar absorption features fall very close to the wavelength predicted by Crutcher's relation (1982), confirming its validity in the solar neighborhood. The eight new lines of sight explored are consistent with the sun embedded in, and at the edge of a warm cloud, and an extension of 20-30 pc for this warm cloud in the direction of Omicron Sgr, and as little as 6 pc in the direction of Beta Hyi and HD 81101, is suggested. The Mg II absorption features are shown to strongly affect the chromospheric emission profiles for cool stars. Future application to Space Telescope observations is suggested for the present velocity separation technique.