Processes and compositions are provided for decreasing emissions of mercury upon combustion of fuels such as coal. Various sorbent compositions are provided that contain components that reduce the level of mercury and/or sulfur emitted into the atmosphere upon burning of coal. In various embodiments, the sorbent compositions are added directly to the fuel before combustion; are added partially to the fuel before combustion and partially into the flue gas post combustion zone; or are added completely into the flue gas post combustion zone. In preferred embodiments, the sorbent compositions comprise a source of halogen and preferably a source of calcium. Among the halogens, iodine and bromine are preferred. In various embodiments, inorganic bromides make up a part of the sorbent compositions.