We propose several self-stabilizing protocols for unidirectional, anonymous, and uniform synchronous rings of arbitrary size, where processors communicate by exchanging messages. When the size of the ring n is unknown, we better the service time by a factor of n (performing the best possible complexity for the stabilization time and the memory consumption). When the memory size is known, we present a protocol that is optimal in memory (constant and independant of n), stabilization time, and service time (both are in Theta(n)).