The present invention are methods for removing preselected substances from a mixed flue gas stream characterized by cooling said mixed flue gas by direct contact with a quench liquid to condense at least one preselected substance and form a cooled flue gas without substantial ice formation on a heat exchanger. After cooling additional process methods utilizing a cryogenic approach and physical concentration and separation or pressurization and sorbent capture may be utilized to selectively remove these materials from the mixed flue gas resulting in a clean flue gas.