Let G be a classical Q-isotropic algebraic group and G(A) be the group of adele-points of G. In the 1980's Roger Howe defined a notion of rank for irreducible unitary representations of G(A) and its local components G(R) and G(Q_p). Among many other results, he proved that for an automorphic representation of G(A) all of these ranks are equal. The latter technique has found a number of applications, namely in the study of multiplicities of automorphic forms, Howe duality, etc. In this talk we extend the rigidity result of Howe in a uniform and conceptual way to include exceptional G. Our approach is based on the orbit method for nilpotent (real and p-adic) Lie groups. In the real case, one needs functional calculus on Lie groups, and in the p-aid case one needs to analyze representations of certain Hecke algebras of bi-invariant functions. As a special case of our result, we obtain a new proof of the following theorem due to Kazhdan (and Gan and Savin): if one local component of a unitary representation of G(A) is "minimal", then all of its local components are "minimal".