diff --git a/compareECLFiles.cmake b/compareECLFiles.cmake
index 2f8e22ea7..54165923d 100644
--- a/compareECLFiles.cmake
+++ b/compareECLFiles.cmake
@@ -27,7 +27,7 @@ macro (add_test_compareECLFiles casename filename simulator abs_tol rel_tol pref
     set(DIR ${casename})
   endif()
   if(${ARGC} GREATER 8)
-    set(TEST_ARGS ${OPM_DATA_ROOT}/${DIR}/${ARGV1} deckfilename=${OPM_DATA_ROOT}/${DIR}/${filename})
+    set(TEST_ARGS ${OPM_DATA_ROOT}/${DIR}/${ARGV8} deck_filename=${OPM_DATA_ROOT}/${DIR}/${filename}.DATA)
   else()
     set(TEST_ARGS ${OPM_DATA_ROOT}/${DIR}/${filename})
   endif()
@@ -113,8 +113,8 @@ add_test_compareECLFiles(spe3 SPE3CASE1 flow_legacy ${abs_tol} ${rel_tol} compar
 add_test_compareECLFiles(spe9 SPE9_CP_SHORT flow_ebos ${abs_tol} ${rel_tol} compareECLFiles "")
 add_test_compareECLFiles(spe9 SPE9_CP_SHORT flow_legacy ${abs_tol} ${rel_tol} compareECLFiles "")
 add_test_compareECLFiles(msw_2d_h 2D_H__ flow_multisegment ${abs_tol} ${rel_tol} compareECLFiles "")
-add_test_compareECLFiles(polymer_simple2D 2D_THREEPHASE_POLY_HETER flow_polymer ${abs_tol} ${rel_tol} compareECLFiles "" polymer_simple2D run.param)
-add_test_compareECLFiles(spe5 SPE5CASE1 flow_solvent ${abs_tol} ${rel_tol} compareECLFiles "")
+add_test_compareECLFiles(polymer_simple2D 2D_THREEPHASE_POLY_HETER flow_polymer ${abs_tol} ${rel_tol} compareECLFiles "")
+add_test_compareECLFiles(spe5 SPE5CASE1 flow_solvent ${abs_tol} ${rel_tol} compareECLFiles "" spe5 run.param)
 
 # Restart tests
 opm_set_test_driver(${PROJECT_SOURCE_DIR}/tests/run-restart-regressionTest.sh "")
diff --git a/opm/autodiff/BlackoilModelEbos.hpp b/opm/autodiff/BlackoilModelEbos.hpp
index 6b7d3383c..6f2b9350c 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_strict_iter_)
+                converged = converged && converged_CNV;
 
             if ( terminal_output_ )
             {
diff --git a/opm/autodiff/BlackoilModelParameters.cpp b/opm/autodiff/BlackoilModelParameters.cpp
index 6ae955458..9808556a7 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_strict_iter_ = param.getDefault("max_strict_iter",8);
         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..cfb36728b 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 on the CNV convergence criterion
+        int max_strict_iter_;
+
         /// Solve well equation initially
         bool solve_welleq_initially_;
 
diff --git a/opm/autodiff/NonlinearSolver_impl.hpp b/opm/autodiff/NonlinearSolver_impl.hpp
index cc6126a01..1caaa0ece 100644
--- a/opm/autodiff/NonlinearSolver_impl.hpp
+++ b/opm/autodiff/NonlinearSolver_impl.hpp
@@ -184,7 +184,7 @@ namespace Opm
         relax_max_       = 0.5;
         relax_increment_ = 0.1;
         relax_rel_tol_   = 0.2;
-        max_iter_        = 15;
+        max_iter_        = 10;
         min_iter_        = 1;
     }