In surgery simulation, precise contact modeling is essential to obtain both realistic behavior and convincing haptic feedback. When instruments create deformations on soft tissues, they modify the boundary conditions of the models and will mainly modify their behavior. Yet, most recent work has focused on the more precise modeling of soft tissues while improving efficiency; but this effort is ruined if boundary conditions are ill-defined. In this paper, we propose a novel and very efficient approach for precise computation of the interaction between organs and instruments. The method includes an estimation of the contact compliance of the concerned zones of the organ and of the instrument. This compliance is put in a buffer and is the heart of the multithreaded local model used for haptics. Contact computation is then performed in both simulation and haptic loops. It follows unilateral formulation and allows realistic interactions on non-linear models simulated with stable implicit scheme of time integration. An iterative solver, initialized with the solution found in the simulation, allows for fast computation in the haptic loop. We obtain realistic and physical results for the simulation and stable haptic rendering.