The authors compute directly the index of Lie algebras \(\mathfrak g\) with \(\dim\mathfrak g<5\). They also compute the index of the generalized Heisenberg algebra and then pass to corresponding computations for (isomorphism classes of) filiform Lie algebras, the subclass of nilpotent Lie algebras with the largest nilindex. Finally they prove that the index of a Lie algebra decreases by deformation.