  Given a $K$-type $\pi$, it is known that its spin norm (due to first-named
author) is lower bounded by its lambda norm (due to Vogan). That is,
$\|\pi\|_{\rm spin}\geq \|\pi\|_{\rm lambda}$. This note aims to describe for
which $\pi$ one can actually have equality. We apply the result to tempered
Dirac series. In the case of real groups, we obtain that the tempered Dirac
series are divided into $\#W^1$ parts among all tempered modules with real
infinitesimal characters.
