  We describe the canonical weak distributive law $\delta \colon \mathcal S
\mathcal P \to \mathcal P \mathcal S$ of the powerset monad $\mathcal P$ over
the $S$-left-semimodule monad $\mathcal S$, for a class of semirings $S$. We
show that the composition of $\mathcal P$ with $\mathcal S$ by means of such
$\delta$ yields almost the monad of convex subsets previously introduced by
Jacobs: the only difference consists in the absence in Jacobs's monad of the
empty convex set. We provide a handy characterisation of the canonical weak
lifting of $\mathcal P$ to $\mathbb{EM}(\mathcal S)$ as well as an algebraic
theory for the resulting composed monad. Finally, we restrict the composed
monad to finitely generated convex subsets and we show that it is presented by
an algebraic theory combining semimodules and semilattices with bottom, which
are the algebras for the finite powerset monad $\mathcal P_f$.
