Two studies of the effect of changing CH4 fluxes on global tropospheric oxidant levels, O3, OH, H2O2, have been performed with a multi-box photochemical model. (1) A sensitivity study is made by scaling back CH4, CO and NO emissions relative to present-day budgets. When the CH4 ice core record is compared to calculated CH4 abundances, corresponding CH4 fluxes for the pre-industrial Holocene (PIH) and Last Glacial Maximum (LGM) are fairly well-constrained: 175–225 Tg CH4/yr for PIH and 100–130 Tg CH4/yr for LGM. Except for OH at fluxes of 100–200 Tg CH4/yr, preindustrial oxidant concentrations levels are not narrowly defined by the CH4 record. The small range of CH4 flux and OH abundance at the LGM is due to strong CH4–OH feedbacks. (2) Specific scenarios for CH4/CO/NO are selected to represent sources for the PIH and LGM. The CH4 budget is taken from an evaluation of wetlands and other natural sources. For CO and NO, apparent O3 levels and ice-core-derived H2O2 for the PIH are used to constrain PIH CO and NO fluxes. These fluxes are further scaled back to simulate the LGM, and perturbed temperature, precipitation and stratosphere-troposphere exchange are prescribed according to the GISS GCM. For the PIH changes for global abundance relative to present day are: 44% less O3; 20% more OH and 56% less H2O2. For the LGM, with 120 Tg CH4/yr and surface temperature 4–5 K lower than today, global changes are 56% less O3, 32% more OH and 59% less H2O2. Calculated preindustrial oxidant changes are in reasonable agreement with other studies based on one-, two- and three-dimensional models, although differences among model physics preclude a definitive comparison. There is consensus that OH has decreased since the Last Glacial Maximum, in contrast to projections for future OH, on which models are in disagreement. Model validation of oxidant concentrations requires more ice-core data. Preindustrial OH would be inferred best by using a model with ice-core measurements of species that are uncoupled from the CH4–CO–OH–O3 cycle. Candidates might be marine gases of moderately long lifetime, e.g., CH3Cl or OCS.