This paper focuses on ‘minimality’ in initial references to persons in the Mayan language Tzeltal, spoken in southern Mexico. Inspection of initial person-referring expressions in 25 Tzeltal videotaped conversations reveals that, in this language, if speaker and/or recipient are related through ‘kinship’ to the referent, a kin term (or other relational term like ‘namesake’) is the default option for initial reference to persons. Additionally, further specification via names and/or geographical location (of home base) is also often used to home in on the referent (e.g. ‘your-cousin Alonzo’, ‘our mother’s brother behind the mountain’). And often (~ 70 cases in the data examined) initial references to persons combine more than one referring expression, for example: ‘this old man my brother-in-law old man Antonio here in the pines’, or ‘the father of that brother-in-law of yours the father-in-law of your elder-sister Xmaruch’. Seen in the light of Schegloff’s (1979, 1996) two basic preferences for referring to persons in conversation: (i.) for a recognitional form and (ii.) for a minimal form, these Tzeltal person-referring expressions seem to be relatively elaborated. This paper examines the sequential contexts where such combinations appear, and proposes a third preference operative in Tzeltal (and possibly in other kinship-term-based systems) for associating the referent as closely as possible to the participants.