  Let G be a reductive p-adic group. We study how a local Langlands
correspondence for irreducible tempered G-representations can be extended to a
local Langlands correspondence for all irreducible smooth representations of G.
We prove that, under a natural condition involving compatibility with
unramified twists, this is possible in a canonical way.
  To this end we introduce analytic R-groups associated to non-tempered
essentially square-integrable representations of Levi subgroups of G. We
establish the basic properties of these new R-groups, which generalize
Knapp--Stein R-groups.
