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We consider finite-dimensional irreducible transitive graded Lie algebras L = r i=−q Li over algebraically closed fields of characteristic three. We assume that the null component L0 is classical and reductive. The adjoint representation of L on itself induces a representation of the commutator subalgebra L ′ 0 of the null component on the minus-one component L−1. We show that if the depth q of L is greater than one, then this representation must be restricted.Over algebraically closed fields F of characteristic p > 0, the classification of the finite-dimensional simple Lie algebras relies on the classification of the finite-dimensional irreducible transitive graded Lie algebras L = r i=−q L i of depth q ≧ 1 with classical reductive null component L 0 . We recall some of the progress that has been made in the classification of such Lie algebras L. In the case in which L −1 is not only irreducible but also restricted as an L 0 -module, such

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