  A classical tool in the study of real closed fields are the fields $K((G))$
of generalised power series (i.e., formal sums with well-ordered support) with
coefficients in a field $K$ of characteristic 0 and exponents in an ordered
abelian group $G$. A fundamental result of Berarducci ensures the existence of
irreducible series in the subring $K((G^{\leq 0}))$ of $K((G))$ consisting of
the generalised power series with non-positive exponents.
  It is an open question whether the factorisations of a series in such subring
have common refinements, and whether the factorisation becomes unique after
taking the quotient by the ideal generated by the non-constant monomials. In
this paper, we provide a new class of irreducibles and prove some further cases
of uniqueness of the factorisation.
