I'll first give some background about concrete rank-1 systems (each such system can be viewed as a measure-preserving transformation on a standard Lebesgue space and can also be viewed as a homeomorphism of a Cantor space). Then I'll describe a simple condition on the canonical generating sequence of a concrete rank-1 system which guarantees that the concrete rank-1 system has trivial centralizer in the group of measure-preserving transformations.