  Let $k$ be a field of characteristic $p$, let $P$ be a finite $p$- group,
where $p$ is an odd prime, and let $D(P)$ be the Dade group of endo-permutation
$kP$-modules. It is known that $D(P)$ is detected via deflation--restriction by
the family of all sections of $P$ which are elementary abelian of rank $\leq2$.
In this paper, we improve this result by characterizing $D(P)$ as the limit
(with respect to deflation--restriction maps and conjugation maps) of all
groups $D(T/S)$ where $T/S$ runs through all sections of $P$ which are either
elementary abelian of rank $\leq3$ or extraspecial of order $p^3$ and exponent
$p$.
