diff --git a/opm/autodiff/BlackoilModelEbos.hpp b/opm/autodiff/BlackoilModelEbos.hpp
index 6b7d3383c..6b115a9a9 100644
--- a/opm/autodiff/BlackoilModelEbos.hpp
+++ b/opm/autodiff/BlackoilModelEbos.hpp
@@ -975,7 +975,12 @@ namespace Opm {
                 residual_norms.push_back(CNV[compIdx]);
             }
 
-            const bool converged = converged_MB && converged_CNV && converged_Well;
+            bool converged = converged_MB && converged_Well;
+
+            // do not care about the cell based residual in the last two Newton
+            // iterations
+            if (iteration < param_.max_iter_ - 2)
+                converged = converged && converged_CNV;
 
             if ( terminal_output_ )
             {
diff --git a/opm/autodiff/BlackoilModelParameters.cpp b/opm/autodiff/BlackoilModelParameters.cpp
index 6ae955458..e33a4c4d2 100644
--- a/opm/autodiff/BlackoilModelParameters.cpp
+++ b/opm/autodiff/BlackoilModelParameters.cpp
@@ -52,6 +52,7 @@ namespace Opm
         tolerance_well_control_ = param.getDefault("tolerance_well_control", tolerance_well_control_);
         maxSinglePrecisionTimeStep_ = unit::convert::from(
                 param.getDefault("max_single_precision_days", unit::convert::to( maxSinglePrecisionTimeStep_, unit::day) ), unit::day );
+        max_iter_ = param.getDefault("max_iter",15);
         solve_welleq_initially_ = param.getDefault("solve_welleq_initially",solve_welleq_initially_);
         update_equations_scaling_ = param.getDefault("update_equations_scaling", update_equations_scaling_);
         use_update_stabilization_ = param.getDefault("use_update_stabilization", use_update_stabilization_);
diff --git a/opm/autodiff/BlackoilModelParameters.hpp b/opm/autodiff/BlackoilModelParameters.hpp
index 9f3427bb9..12260472a 100644
--- a/opm/autodiff/BlackoilModelParameters.hpp
+++ b/opm/autodiff/BlackoilModelParameters.hpp
@@ -56,6 +56,9 @@ namespace Opm
         /// for solving for the Jacobian
         double maxSinglePrecisionTimeStep_;
 
+        /// Maximum number of Newton iterations before we give up
+        int max_iter_;
+
         /// Solve well equation initially
         bool solve_welleq_initially_;