  We present results for spectroscopic factors of the outermost shells in
$^{40}$Ca and $^{208}$Pb, which have been derived from the comparison between
the available quasielastic ($e,e'p$) data from NIKHEF-K and the corresponding
calculated cross-sections obtained within a fully relativistic formalism. We
include exactly the effect of Coulomb distortion on the electron wave functions
and discuss its role in the extraction of the spectroscopic factors from
experiment. Without any adjustable parameter, we find spectroscopic factors of
about 70\%, consistent with theoretical predictions. We compare our results
with previous relativistic and nonrelativistic analyses of ($e,e'p$) data. In
addition to Coulomb distortion effects we discuss different choices of the
nucleon current operator and also analyze the effects due to the relativistic
treatment of the outgoing-distorted and bound nucleon wave functions.
