  The minimal faithful permutation degree $\mu(G)$ of a finite group $G$ is the
least nonnegative integer $n$ such that $G$ embeds in the symmetric group
$\Sym(n)$. Clearly $\mu(G \times H) \le \mu(G) + \mu(H)$ for all finite groups
$G$ and $H$. Wright (1975) proves that equality occurs when $G$ and $H$ are
nilpotent and exhibits an example of strict inequality where $G\times H$ embeds
in $\Sym(15)$.
  Saunders (2010) produces an infinite family of examples of permutation groups
$G$ and $H$ where $\mu(G \times H) < \mu(G) + \mu(H)$, including the example of
Wright's as a special case. The smallest groups in Saunders' class embed in
$\Sym(10)$. In this paper we prove that 10 is minimal in the sense that $\mu(G
\times H) = \mu(G) + \mu(H)$ for all groups $G$ and $H$ such that $\mu(G\times
H)\le 9$.
