Abstract : On a p-adic vector space $V$, for a contracting $\tau\in GL(V)$, we introduce nested subclasses of $\tau$-decomposable embeddable measures $L_m^\#(\tau)$, $-1\leq m\leq\infty$, characterise them in terms of L\'evy measures and show that $L_\infty^\#(\tau)$ is the smallest closed $\tau$-invariant semigroup containing all $\tau$-semistable measures and all $\tau$-decomposable idempotents.