  A simple technique is described that provides an improved nearside-farside
(NF) method for elastic scattering amplitudes. The technique, involving the
novel resummation of a Legendre partial wave series, reduces the importance of
unphysical contributions to NF subamplitudes, which can arise in more
conventional NF decompositions. Detailed applications are made to a strong
absorption model and to a ^{16}O + ^{16}O optical potential at E_{lab} = 145
MeV. We also discuss ^{16}O + ^{16}O at E_{lab} = 480, 704, 1120 MeV, and alpha
+ ^{12}C, alpha + ^{40}Ca, both at E_{lab} = 1370 MeV.
