diff --git a/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h b/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h
index dbe97745c3d..5e7868bb263 100644
--- a/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h
+++ b/Triangulation_3/test/Triangulation_3/include/CGAL/_test_cls_regular_euclidean_traits_3.h
@@ -148,6 +148,7 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   Bare_point q3(0.,0.,2.);
   Bare_point q4(2.,2.,2.);
   Bare_point q5(-2.,0.,0.);
+  Bare_point q6(-4.,0.,0.);
 
   Weighted_point wq0(q0,0.);
   Weighted_point wq1(q1,0.);
@@ -155,6 +156,7 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   Weighted_point wq3(q3,0.);
   Weighted_point wq4(q4,0.);
   Weighted_point wq5(q5,0.);
+  Weighted_point wq6(q6,0.);
   Weighted_point wq01(q0,2.);
   Weighted_point wq11(q1,2.);
   Weighted_point wq21(q2,2.);
@@ -244,13 +246,21 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   
   // test power_test
   // null weights
-  assert(power_test(wq0,wq1,wq2,wq3,wq4) ==
-         traits.side_of_oriented_sphere_3_object()(q0,q1,q2,q3,q4));
-  assert(power_test(wq1,wq0,wq2,wq3,wq4) ==
-         traits.side_of_oriented_sphere_3_object()(q1,q0,q2,q3,q4));
-  assert(power_test(wq0,wq1,wq2,wq3) ==
-         traits.coplanar_side_of_bounded_circle_3_object()(q0,q1,q2,q3));
-  assert(power_test(wq5,wq1,wq0) == (Segment_3(wq5,wq1)).has_on(wq0));
+  assert(power_test(wq0,wq1,wq2,wq3,wq4) == CGAL::ON_ORIENTED_BOUNDARY &&
+         traits.side_of_oriented_sphere_3_object()(q0,q1,q2,q3,q4) ==
+                                                             CGAL::ON_BOUNDARY);
+  assert(power_test(wq1,wq0,wq2,wq3,wq6) == CGAL::ON_POSITIVE_SIDE &&
+         traits.side_of_oriented_sphere_3_object()(q1,q0,q2,q3,q6) ==
+                                                         CGAL::ON_BOUNDED_SIDE);
+  assert(power_test(wq0,wq1,wq2,wq5) == CGAL::ON_NEGATIVE_SIDE &&
+         traits.coplanar_side_of_bounded_circle_3_object()(q0,q1,q2,q5) ==
+                                                       CGAL::ON_UNBOUNDED_SIDE);
+  assert(power_test(wq5,wq1,wq0) == CGAL::ON_POSITIVE_SIDE &&
+         (Segment_3(wq5,wq1)).has_on(wq0));
+  assert(power_test(wq5,wq1,wq5) == CGAL::ON_ORIENTED_BOUNDARY &&
+         (Segment_3(wq5,wq1)).has_on(wq5));
+  assert(power_test(wq5,wq1,wq6) == CGAL::ON_NEGATIVE_SIDE &&
+         !(Segment_3(wq5,wq1)).has_on(wq6));
   assert(power_test(wq3,wq2) == CGAL::ON_ORIENTED_BOUNDARY);
 
   // wc = (1,1,1) -3
@@ -266,19 +276,19 @@ _test_cls_regular_euclidean_traits_3 (const Traits &)
   wc = Weighted_point(weighted_circumcenter(wp01,wp1,wq21),
                       squared_radius_smallest_orthogonal_sphere(wp01,wp1,wq21));
   assert(power_test(wp01,wp1,wq21,wc) == CGAL::ON_NEGATIVE_SIDE);
-  wc = Weighted_point(Bare_point(-1.,1.,0.),6);
-  assert(power_test(wp01,wp1,wq21,wc) == CGAL::ON_ORIENTED_BOUNDARY);
-  wc = Weighted_point(Bare_point(3.,4.,0.),10);
-  assert(power_test(wp01,wp1,wq21,wc) == CGAL::ON_POSITIVE_SIDE);
+  wt = Weighted_point(Bare_point(-1.,1.,0.),6);
+  assert(power_test(wp01,wp1,wq21,wt) == CGAL::ON_ORIENTED_BOUNDARY);
+  wt = Weighted_point(Bare_point(3.,4.,0.),10);
+  assert(power_test(wp01,wp1,wq21,wt) == CGAL::ON_POSITIVE_SIDE);
 
   // wc = (0,0,3) -9
   wc = Weighted_point(weighted_circumcenter(wp04,wp3),
                       squared_radius_smallest_orthogonal_sphere(wp04,wp3));
   assert(power_test(wp04,wp3,wc) == CGAL::ON_NEGATIVE_SIDE);
-  wc = Weighted_point(Bare_point(0.,0.,7.),25);
-  assert(power_test(wp04,wp3,wc) == CGAL::ON_ORIENTED_BOUNDARY);
-  wc = Weighted_point(Bare_point(0.,0.,2.),12);
-  assert(power_test(wp04,wp3,wc) == CGAL::ON_POSITIVE_SIDE);
+  wt = Weighted_point(Bare_point(0.,0.,7.),25);
+  assert(power_test(wp04,wp3,wt) == CGAL::ON_ORIENTED_BOUNDARY);
+  wt = Weighted_point(Bare_point(0.,0.,2.),12);
+  assert(power_test(wp04,wp3,wt) == CGAL::ON_POSITIVE_SIDE);
 
   assert(power_test(wq0,wq02) == CGAL::ON_POSITIVE_SIDE);
   assert(power_test(wq01,wq01) == CGAL::ON_ORIENTED_BOUNDARY);