  We address two fundamental questions in the representation theory of affine
Hecke algebras of classical types. One is an inductive algorithm to compute
characters of tempered modules, and the other is the determination of the
constants in the formal degrees of discrete series (in the form conjectured by
Reeder \cite{Re}). The former is completely different than the Lusztig-Shoji
algorithm \cite{Sh, L}, and it is more effective in a number of cases. The main
idea in our proof is to introduce a new family of representations which behave
like tempered modules, but for which it is easier to analyze the effect of
parameter specializations. Our proof also requires a comparison of the
$C^{\ast}$-theoretic results of Opdam, Delorme, Slooten, Solleveld \cite{O, DO,
Sl2, OSa, OS}, and the geometric construction from \cite{K1,K2,CK}.
