A contaminant, such as sulfur dioxide, is removed from a fluid, such as hot exhaust gas, by passing it through beds of material for removing the contaminants, such as activated carbon for adsorbing the sulfur dioxide as sulfur trioxide; periodically, the bed is regenerated by discontinuing the passage of process fluid therethrough and passing through the bed a regenerating fluid, such as water, with quantities of the regenerating fluid being successively passed through the bed with corresponding decreasing amounts of contaminants, such as sulfuric acid within the water, in the respective quantities of regenerative fluid. At least one further bed of material is regenerated with substantially the same regenerative fluid in substantially the same succession of concentrations, but out of phase so that a quantity of regenerative fluid of one contaminant concentration is passed completely through only one bed of material prior to its passing through another bed of material. Preferably, after passing through one bed of material, the regenerative fluid is of the next highest concentration and passes through another bed of material in the sequence of the next highest concentration.