We describe two new algorithms for implementing barrier synchronization on a shared-memory multicomputer. Both algorithms are based on a method due to \textit{E. D. Brooks} [ibid. 15, 295-307 (1986; Zbl 0641.68010)]. We first improve Brooks' algorithm by introducing double buffering. Our dissemination algorithm replaces Brooks' communication pattern with an information dissemination algorithm described by Hand and Finkel. Our tournament algorithm uses a different communication pattern and generally requires fewer total instructions. The resulting algorithms improve Brooks' original barrier by a factor of two when the number of processes is a power of two. When the number of processes is not a power of two, these algorithms improve even more upon Brooks' algorithm because absent processes need not be simulated. These algorithms share with Brooks' barrier the limitation that each of the n processes meeting at the barrier must be assigned identifiers i such that \(0\leq i