This paper presents the Stars2 corpus of definite descriptions for referring expression generation (REG). The corpus was produced in collaborative communication involving speaker-hearer pairs, and includes situations of reference that are arguably under-represented in similar work. Stars2 is intended as an incremental contribution to the research in REG and related fields, and it may be used both as training/test data for algorithms of this kind, and also to gain further insights into reference phenomena in general, with a particular focus on the issue of attribute choice in referential overspecification.