  We study chiral symmetry breaking in quenched strong-coupling QED$_4$ in
arbitrary covariant gauge within the Dyson-Schwinger equation formalism. A
recently developed numerical renormalization program is fully implemented.
Results are compared for three different fermion-photon proper vertex {\it
Ans\"{a}tze\/}: bare $\gamma^\mu$, minimal Ball-Chiu, and Curtis-Pennington.
The procedure is straightforward to implement and numerically stable. We
discuss the chiral limit and observe that in this limit the renormalized axial
current is conserved. A detailed study of residual gauge dependence due to the
vertex choice is in progress. The relevance for lattice studies is discussed.
