Abstract: A flue gas is cleaned by feeding same to a filtering separator. The filtering separator is accommodated in a housing, and the housing has a pre-filter side ahead of the filtering separator and a clean side following the filtering separator in the flue gas flow direction. A filter element has an adsorbent formed of dust-free spheroidal charcoal on the clean side of the housing. The flue gas flows through the adsorbent in the filter element. Harmful substances from the group including mercury and/or dioxin and/or furan and/or further heavy metals are thereby removed from the flue gas.