  The renormalization of iterated one-pion exchange (OPE) is studied in Chiral
Effective Field Theory ($\chi$EFT) for the antinucleon-nucleon
($\overline{N}\!N$) system. The OPE potential is cut off at a certain distance
and contact interactions are represented by a complex spherical well with the
same radius. We investigate the dependence on the cutoff radius of the phase
shifts, inelasticities, and mixing angles for the low partial waves in
$\overline{N}\!N$ scattering. We show that renormalization requires additional
contact interactions compared to the expectation based on naive dimensional
analysis. Results after renormalization are compared with the state-of-the-art
energy-dependent partial-wave analysis of $\overline{N}\!N$ data. We compare
our conclusions with applications of $\chi$EFT to the nucleon-nucleon system.
