The bond-order indices derived from the displacements DeltaGamma= Gamma - Gamma(0) of the pair-diagonal part of the two-electron density matrix Gamma in the orthogonalized atomic orbital (OAO) representation, relative to the atomic promolecule reference Gamma(0), are reexamined. The corresponding sum rules are discussed and the new index J = trDeltaGamma is introduced. The entropy deficiency interpretation of the bond entropy is given and the information measures of bond multiplicity are approximately related to DeltaGamma. Illustrative results for model systems, including 2- and 3-OAO models and pi-electron systems in the Huckel approximation, demonstrate that these two-electron indices compare favorably with chemical intuition. (C) 2004 Elsevier B.V. All rights reserved.