A one-step reduced mechanism for hydrogen combustion, previously developed for fuel-lean flames, is extended to apply for all equivalence ratios under near-limit conditions by taking into consideration two additional recombination steps that are important under fuel-rich conditions. It is found that the crossover temperature that appears in the cutoff factor is smaller under fuel-rich conditions. Besides improving insights, the results can be beneficial in speeding computations. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.