  This contribution focuses on two-party negotiation over continuous issues. We
firstly prove two drawbacks of the jointly Improving Direction Method (IDM),
namely that IDM is not a Strategy-Proof (SP) nor an Information Concealing (IC)
method. Thus we prove that the concurrent lack of these two properties implies
the actual non-efficiency of IDM. Finally we propose a probabilistic method
which is both IC and stochastically SP thus leading to efficient settlements
without being affected by manipulatory behaviors.
