Lynch's vanishing theorem for generalized Whittaker modules applies to generic homomorphisms of the nilradical of a class of parabolic subalgebras which we have named nice. In this talk we describe the classification of nice parabolic subalgebras of simple Lie algebras. Our results give rise to a new characterisation of even nilpotents. We will also give a normal form of Richardson elements for nice parabolic subalgebras in the classical case.