  In 1980 J. Powell proposed that, for every genus $g$, five specific elements
suffice to generate the Goeritz group $\mathcal {G}_g$ of genus $g$ Heegaard
splittings of $S^3$. Powell's Conjecture remains undecided for $g \geq 4$. Let
$\mathcal{P}_g \subset \mathcal {G}_g$ denote the subgroup generated by
Powell's elements. Here we show that, for each genus $g$, the natural function
$\mathcal {G}_g \to \mathcal {G}_{g+1}/\mathcal {P}_{g+1}$ is trivial.
