A derivation is called Jordan decomposable i-f it can be decomposed into a sum of commuting nil and semi-simple parts. In this paper, we study a subfamily of such derivations, the strongly decomposable derivations. After establishing some basic properties, we present an intrinsic criterion for such a derivation. As an application, a classical theorem of Kharchenko on algebraic derivations is sharpened. This and other properties indicate that the notion of strongly decomposable derivations is a natural generalization of algebraic derivations.