diff --git a/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/compute_robustness_benchmark_data.py b/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/compute_robustness_benchmark_data.py
index 9e5fead9f86..9def2bb6cc1 100755
--- a/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/compute_robustness_benchmark_data.py
+++ b/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/compute_robustness_benchmark_data.py
@@ -23,18 +23,19 @@ def compute_robustness_benchmark_data(execname, filename, alpha, max_time):
 
   exit_codes = {
    0 : "VALID_SOLID_OUTPUT",
-   1 : "OUTPUT_IS_NOT_TRIANGLE_MESH",
-   2 : "OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD",
-   3 : "OUTPUT_HAS_BORDERS",
-   4 : "OUTPUT_HAS_DEGENERATED_FACES",
-   5 : "OUTPUT_HAS_GEOMETRIC_SELF_INTERSECTIONS",
-   6 : "OUTPUT_DOES_NOT_BOUND_VOLUME",
-   7 : "OUTPUT_DOES_NOT_CONTAIN_INPUT",
-   8 : "OUTPUT_DISTANCE_IS_TOO_LARGE",
-   9 : "SIGSEGV",
-   10 : "SIGABRT",
-   11 : "SIGFPE",
-   12 : "TIMEOUT"
+   1 : "INPUT_IS_INVALID",
+   2 : "OUTPUT_IS_NOT_TRIANGLE_MESH",
+   3 : "OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD",
+   4 : "OUTPUT_HAS_BORDERS",
+   5 : "OUTPUT_HAS_DEGENERATED_FACES",
+   6 : "OUTPUT_HAS_GEOMETRIC_SELF_INTERSECTIONS",
+   7 : "OUTPUT_DOES_NOT_BOUND_VOLUME",
+   8 : "OUTPUT_DOES_NOT_CONTAIN_INPUT",
+   9 : "OUTPUT_DISTANCE_IS_TOO_LARGE",
+   10 : "SIGSEGV",
+   11 : "SIGABRT",
+   12 : "SIGFPE",
+   13 : "TIMEOUT"
   }
 
   exit_code = 0
diff --git a/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/generate_robustness_benchmark_charts.py b/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/generate_robustness_benchmark_charts.py
index da313069594..f9938d4fc7b 100644
--- a/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/generate_robustness_benchmark_charts.py
+++ b/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/generate_robustness_benchmark_charts.py
@@ -40,22 +40,24 @@ def main(argv):
 
   exit_codes = {
    0 : "VALID_SOLID_OUTPUT",
-   1 : "OUTPUT_IS_NOT_TRIANGLE_MESH",
-   2 : "OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD",
-   3 : "OUTPUT_HAS_BORDERS",
-   4 : "OUTPUT_HAS_DEGENERATED_FACES",
-   5 : "OUTPUT_HAS_GEOMETRIC_SELF_INTERSECTIONS",
-   6 : "OUTPUT_DOES_NOT_BOUND_VOLUME",
-   7 : "OUTPUT_DOES_NOT_CONTAIN_INPUT",
-   8 : "OUTPUT_DISTANCE_IS_TOO_LARGE",
-   9 : "SIGSEGV",
-   10 : "SIGABRT",
-   11 : "SIGFPE",
-   12 : "TIMEOUT"
+   1 : "INPUT_IS_INVALID",
+   2 : "OUTPUT_IS_NOT_TRIANGLE_MESH",
+   3 : "OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD",
+   4 : "OUTPUT_HAS_BORDERS",
+   5 : "OUTPUT_HAS_DEGENERATED_FACES",
+   6 : "OUTPUT_HAS_GEOMETRIC_SELF_INTERSECTIONS",
+   7 : "OUTPUT_DOES_NOT_BOUND_VOLUME",
+   8 : "OUTPUT_DOES_NOT_CONTAIN_INPUT",
+   9 : "OUTPUT_DISTANCE_IS_TOO_LARGE",
+   10 : "SIGSEGV",
+   11 : "SIGABRT",
+   12 : "SIGFPE",
+   13 : "TIMEOUT"
   }
 
   current_run_data = {
    "VALID_SOLID_OUTPUT" : 0,
+   "INPUT_IS_INVALID" : 0,
    "OUTPUT_IS_NOT_TRIANGLE_MESH" : 0,
    "OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD" : 0,
    "OUTPUT_HAS_BORDERS" : 0,
diff --git a/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/robustness_benchmark.cpp b/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/robustness_benchmark.cpp
index 57f58b342bd..353e5569d1f 100644
--- a/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/robustness_benchmark.cpp
+++ b/Alpha_wrap_3/benchmark/Alpha_wrap_3/Robustness/robustness_benchmark.cpp
@@ -21,14 +21,15 @@ enum Robustness_benchmark_exit_code
   VALID_SOLID_OUTPUT = 0,
 
   // Failure
-  OUTPUT_IS_NOT_TRIANGLE_MESH = 1,
-  OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD = 2,
-  OUTPUT_HAS_BORDERS = 3,
-  OUTPUT_HAS_DEGENERATED_FACES = 4,
-  OUTPUT_HAS_GEOMETRIC_SELF_INTERSECTIONS = 5,
-  OUTPUT_DOES_NOT_BOUND_VOLUME = 6,
-  OUTPUT_DOES_NOT_CONTAIN_INPUT = 7,
-  OUTPUT_DISTANCE_IS_TOO_LARGE = 8,
+  INTPUT_IS_INVALID = 1,
+  OUTPUT_IS_NOT_TRIANGLE_MESH = 2,
+  OUTPUT_IS_COMBINATORIAL_NON_MANIFOLD = 3,
+  OUTPUT_HAS_BORDERS = 4,
+  OUTPUT_HAS_DEGENERATED_FACES = 5,
+  OUTPUT_HAS_GEOMETRIC_SELF_INTERSECTIONS = 6,
+  OUTPUT_DOES_NOT_BOUND_VOLUME = 7,
+  OUTPUT_DOES_NOT_CONTAIN_INPUT = 8,
+  OUTPUT_DISTANCE_IS_TOO_LARGE = 9,
 };
 
 } // namespace
@@ -58,14 +59,18 @@ int main(int argc, char** argv)
   }
 
   if(argc < 3 || relative_alpha_ratio <= 0.)
-    return AW3i::VALID_SOLID_OUTPUT;
+    return AW3i::INTPUT_IS_INVALID;
 
   Mesh input_mesh;
   if(!PMP::IO::read_polygon_mesh(entry_name_ptr, input_mesh) ||
      is_empty(input_mesh) ||
-     !is_triangle_mesh(input_mesh))
+     !is_triangle_mesh(input_mesh)
+#ifndef CGAL_ALPHA_WRAP_3_TOLERATE_DEGENERACIES
+     || AW3i::has_degenerated_faces(input_mesh)
+#endif
+     )
   {
-    return AW3i::VALID_SOLID_OUTPUT;
+    return AW3i::INTPUT_IS_INVALID;
   }
 
   const CGAL::Bbox_3 bbox = PMP::bbox(input_mesh);