  We describe a condition involving noncommutative Alexander modules which
ensures that a knot with Alexander module $\mathbb{Z}[t^{\pm 1}]/(t-2) \oplus
\mathbb{Z}[t^{\pm 1}]/(t^{-1}- 2)$ is topologically doubly slice. As an
application, we show that a satellite knot $R_\eta(K)$ is doubly slice if the
pattern $R$ has Alexander module $\mathbb{Z}[t^{\pm 1}]/(t- 2) \oplus
\mathbb{Z}[t^{\pm 1}]/(t^{-1}- 2)$ and satisfies this condition, and if the
infection curve $\eta \subset S^3 \setminus R$ lies in the second derived
subgroup $\pi_1(S^3 \setminus R)^{(2)}.$
