The practice of collaboration, and particularly international collaboration, is becoming ever more widespread in scientific research, and is likewise receiving greater interest and stimulus from policy-makers. However, the relation between research performance and degree of internationalization at the level of single researchers still presents unresolved questions. The present work, through a bibliometric analysis of the entire Italian university population working in the hard sciences over the period 2001-2005, seeks to answer some of these questions. The results show that the researchers with top performance with respect to their national colleagues are also those who collaborate more abroad, but that the reverse is not always true. Also, interesting differences emerge at the sectorial level. Finally, the effect of the nation involved in the international partnership plays a role that should not be ignored.