The central issues of this conference, in view of current economic-social environment, are energy efficiency and greenhouse gas emission in ironmaking, i.e. the coal (or carbon) rate. Keeping the goals of sustainable development in mind, current commercial direct reduction and smelting reduction processes, in comparison with blast furnace, will be briefly discussed. In the search of alternatives to blast furnace, the main subject of the present work is to assess options of making hot metal from iron ore and coal directly along selected theoretical paths under ideal conditions. Professor Sven Eketorp's proposal published in 1968 that for minimum carbon rate in ironmaking, carbon should be used as reductant first and the reaction product carbon monoxide as fuel next at 100% degree of post-combustion (in an order which is opposite to that in blast furnace). It is an important guidance in the searching for a process which could be more efficient, in principle, than blast furnace. The idealization of processes includes the assumptions of adiabatic condition, perfect heat transfer and using carbon and hematite instead of coal and ore; and that problems related to refractory, mechanical equipment, any particular environment regulations are ignored in this work. The theoretical frame work of two approaches of hot metal production for steelmaking, based on iron ore and coal directly (without coking and sintering) will be examined. These two chosen representative routes are: (1) It starts with smelting reduction of iron oxides (after varying degree of pre-reduction) with carbon to produce liquid iron; and for improving overall energy efficiency gaseous product from smelting reduction vessel is used to carry out pre-reduction of iron oxides in another reactor to lower the work load (i.e., carbon rate) of the vessel. (2) It starts with direct reduction of hematite by heating hematite/carbon composite agglomerates to produce DRI and followed by melting of fully metallized DRI in an oxy-coal converter to obtain liquid iron. These fundamental properties of idealized and coupled two-reactor systems could be considered the theoretical foundations from which more efficient ironmaking processes as alternatives to blast furnace might be successfully developed.