  Let G be an orthogonal or symplectic p-adic group (not necessarily split) or
an inner form of a general linear p-adic group. In a previous paper, it was
shown that the Bernstein components of the category of smooth representations
of G are equivalent to the category of right modules over some Hecke algebra
with parameters, or more general over the semi-direct product of such an
algebra with a finite group algebra. The aim of the present paper is to show
that this equivalence preserves the tem- pered spectrum and the discrete series
representations.
