  Let $p$ be a prime and $\mathbb{F}$ a field of characteristic $p$, and let
$\mathcal{H}_n$ denote the Iwahori--Hecke algebra of the symmetric group
$\mathfrak{S}_n$ over $\mathbb{F}$ at $q=-1$. We prove that there are only
finitely many partitions $\lambda$ such that both $\lambda$ and $\lambda'$ are
2-singular and the Specht module $S^\lambda$ for $\mathcal{H}_{|\la|}$ is
irreducible.
