This paper describes and compares two compile-time analysis algorithms for deriving the path modes of a moded concurrent logic program. A path describes a subterm of a procedure argument. Deriving all path modes is a way to perform certain valuable optimizations, such as sequentialization of too-fine concurrent tasks, and scheduling to reduce suspension. We describe our own variation of Ueda and Morita's original constraint propagation scheme, which includes our novel circular unification algorithm. We also describe an alternative method of finite domain analysis that we developed. The two methods are critiqued and we show the relationship between them.