  Let $E$ be an elliptic curve defined over a number field $K$ with
supersingular reduction at all primes of $K$ above $p$. If $K_{\infty}/K$ is a
$\mathbb{Z}_p$-extension such that $E(K_{\infty})[p^{\infty}]$ is finite and
$H^2(G_S(K_{\infty}), E[p^{\infty}])=0$, then we prove that the
$\Lambda$-torsion subgroup of the Pontryagin dual of
$\text{Sel}_{p^{\infty}}(E/K_{\infty})$ is pseudo-isomorphic to the Pontryagin
dual of the fine Selmer group of $E$ over $K_{\infty}$. This is the
Galois-cohomological analog of a flat-cohomological result of Wingberg.
