It is shown that, given suitable radial velocity values for the stars and the local interstellar medium (LISM) interstellar absorption can be distinguished from chromospheric self absorption within the MgII emissions from late type stars. Beta Hyi (G2IV) offers a clear example. Zeta Tuc (G2V) and delta Pav (G8V) which are very close to beta Hyi show similar narrow MgII absorption features, which are also interpretable as interstellar. Narrow MgII absorptions in the rapidly rotating F-type stars beta TrA and alpha Hyi are reported. The absence of IS Mg II in the stars tau Cet and 24UMa confirms the presence of a hole in the LISM near galactic longitude 150 deg.