  A recently derived dispersive optical model potential (DOMP) for $^{208}$Pb
is extended to consider the non-locality in the real potential and the
shell-gap in the definition of the nuclear imaginary potentials near the Fermi
energy. The modified DOMP improves the simultaneous description of nucleon
scattering on $^{208}$Pb and of the $^{208}$Pb particle-hole bound states. The
new potential is shown to give a very good description of nucleon scattering
data on near-magic targets $^{206,207}$Pb and $^{209}$Bi.
