Dry processes, apparatus, compositions and systems are provided for reducing emissions of sulfur oxides, and sulfur dioxide in particular, and/or HCl and/or Hg in a process employing a combination of a lime-based sorbent, in particular hydrated lime and/or dolomitic hydrated lime, and a sorbent doping agent administered to achieve coverage of a three-dimensional cross section of a passage carrying SOx and/or HCl and/or Hg-containing gases with a short but effective residence time at a temperature effective to provide significant sulfur dioxide and/or HCl and/or Hg reductions with high rates of reaction and sorbent utilization. The once-through, dry process can advantageously introduce the sorbent and sorbent doping agent dry or preferably as a slurry to enable uniform treatment. Preferred sorbent doping agents include water-soluble or water-dispersible copper and/or iron compositions which can be heated to an active form in situ by the flue gases being treated.