We propose three small sets of barrier heights for heavy-atom transfer, nucleophilic substitution, and unimolecular and association reactions as benchmarks for comparing and developing theoretical methods. We chose the data sets to be statistically representative subsets of the NHTBH38/04 database. Each data set consists of 6 barrier heights; we call these small benchmark suites HATBH6, NSBH6, and UABH6. Benchmark values are tabulated for 205 combinations of theory level and basis set. The theory levels studied include single-level wave function theory like Hartree-Fock, Møller-Plesset perturbation theory, quadratic configuration interaction, and coupled cluster theory; they also include multicoefficient correlation methods, local and hybrid density functional theory, and semiempirical molecular orbital methods. The three new representative data sets are combined with a previous representative data set for hydrogen-transfer reactions to form a new compact but diverse and representative data set called DBH24. Comparison of a large number of methods for their performance on DBH24 leads us to recommend the following methods for barrier height calculations, in order of decreasing cost: G3SX, BMC-CCSD, PWB6K, BB1K, M06-L, MPW1K, HF/MIDII, and PM3.