ac.commutative algebra - Lifting results from smooth maps to essentially smooth maps.

Recall that a morphism of rings $Rto S$ is called (essentially) smooth if it is formally smooth and (essentially) finitely presented.

(Note: $Rto S$ is essentially finitely presented provided that $S$ is the localization of some finitely
presented $R$-algebra $T$ at some multiplicative system $A subset T$, that is, $S=A^{-1}T$.)

In class, our professor said that working with smooth or essentially smooth morphisms yields an effectively equivalent theory. This motivates my question: Is there a general technique to lift results from the smooth case to the essentially smooth case?

Edit: According to Mel, every essentially smooth morphism is a localization of a smooth morphism. However, this direction is much more involved than the other direction, which is immediate from the definitions. Anyway, this would be the answer to the question.