This method relies on the idea that deoxidation of slag will lead to the deoxidation of steel.
The chemical equilibrium equation used for this process is:
where a is the activity of the oxygen in the slag, and a is the activity of oxygen in the steel.
Reducing the activity in the slag (a) will lower the oxygen levels in the slag.  Afterwards, oxygen will diffuse from the steel into the lesser concentrated slag.  This method is done by using deoxidizing agents on the slag, such as coke or silicon.  As these agents do not come into direct contact with the steel, non-metallic inclusions will not form in the steel itself.