We compare here the halogen bond characteristics of bimolecular adducts involving either N-bromo- or N-iodosaccharin as strong halogen bond donors, with 4-picoline as a common XB acceptor. In the NBSac·Pic system, the bromine atom of NBSac is displaced toward the picoline, almost at a median position between the two nitrogen atoms, NSac and N'Pic, with NSacBr and BrN'Pic distances at 2.073(6) and 2.098(6) Å respectively. This extreme situation contrasts with the analogous iodine derivative, NISac·Pic, where the NSac-I and IN'Pic distances amount to 2.223(4) and 2.301(4) Å respectively. Periodic DFT calculations, and molecular calculations of adducts (PBEPBE-D2 aug-cc-pVTZ) either at the experimental frozen geometry or with optimization of the halogen position, indicate a more important degree of covalency (i.e. shared-shell character) in the adduct formed with the bromine atom. A stronger charge transfer to the picoline is also found for the bromine (+0.27 |e|) than for the iodine (+0.18 |e|) system. This inversion of halogen bond strength between I and Br finds its origin in the strong covalent character of the interaction in these adducts, in line with the strength of covalent N-Br and N-I bonds. Detailed characterization of the critical points (CPs) of the L(r) = -∇2ρ(r) function along bonding directions has permitted the adducts to be distinguished and they can be respectively described as "neutral" NISac/Pic and "intermediate" NSac/Br/Pic, the latter with Br being close to formal equivalent NSacBr and BrN'Pic interactions but still more associated to the XB donor than to the picoline, as indicated by the topological and energetic properties of the ρ(r) function at the bond critical points (BCPs).