Abstract: Token rotation algorithms play an important role in distributed computing, to support such activities as mutual exclusion, round-robin scheduling, group membership and group communication protocols. Ring-based protocols maximize throughput in busy systems, but can incur a linear, in the number of processors, delay when a processor needs to obtain a token to perform an operation. This paper synthesizes these two algorithmic techniques thereby improving performance (responsiveness) of logical ring protocols. The parameterized technique preserves the safety properties of ring protocols and maintains high throughput in busy systems, while reducing the delay in lightly loaded systems from a linear to the logarithmic function in the number of processors. The algorithmic development is done using term rewriting systems where our parameterized protocol is developed in a series of safety-preserving refinements of a basic specification.