diff --git a/test/multi/algorithms/multi_convex_hull.cpp b/test/multi/algorithms/multi_convex_hull.cpp
index 19d9c1ff6..0da8d0ecf 100644
--- a/test/multi/algorithms/multi_convex_hull.cpp
+++ b/test/multi/algorithms/multi_convex_hull.cpp
@@ -47,9 +47,28 @@ void test_all()
     typedef bg::model::multi_point<P> mp;
     typedef bg::model::multi_linestring<bg::model::linestring<P> > ml;
     typedef bg::model::multi_polygon<bg::model::polygon<P> > mpoly;
-    test_geometry<mp>("multipoint((1.1 1.1), (2.5 2.1), (3.1 3.1), (4.9 1.1), (3.1 1.9))", 5, 4, 3.8);
+
+    // All points below in upper-points and lower-points
+    test_geometry<mp>("MULTIPOINT((0 0),(5 0),(1 1),(4 1))", -1, 5, 4.0);
+    test_geometry<mp>("MULTIPOINT((0 1),(5 1),(1 0),(4 0))", -1, 5, 4.0);
+
+    // All points in vertical line (this delivers an empty polygon with 2 points and a closing point)
+    test_geometry<mp>("MULTIPOINT((1 0),(5 0),(3 0),(4 0),(2 0))", -1, 3, 0.0);
+
+    // One point only
+    test_geometry<mp>("MULTIPOINT((1 0))", -1, 3, 0.0);
+
+    // Problem of 6019, reproduced by the convex hull robustness test:
+    test_geometry<mp>("MULTIPOINT((2 9),(1 3),(9 4),(1 1),(1 0),(7 9),(2 5),(3 7),(3 6),(2 4))", 
+            -1, 6, 48.0);
+
+    // Ticket 6019:
+    test_geometry<mp>("MULTIPOINT((0 53),(0 103),(0 53),(0 3),(0 3),(0 0),(1 0),(1 1),(2 1),(2 0),(2 0),(2 0),(3 0),(3 1),(4 1),(4 0),(5 0),(0 3),(10 3),(10 2),(10 2),(10 2),(5 2),(5 0),(5 0),(55 0),(105 0))", 
+            -1, 4, 5407.5);
     // Ticket 6021:
     test_geometry<mp>("multipoint((0 53), (0 103), (1 53))", 3, 4, 25);
+
+    test_geometry<mp>("multipoint((1.1 1.1), (2.5 2.1), (3.1 3.1), (4.9 1.1), (3.1 1.9))", 5, 4, 3.8);
     test_geometry<ml>("multilinestring((2 4, 3 4, 3 5), (4 3,4 4,5 4))", 6, 5, 3.0);
     test_geometry<mpoly>("multipolygon(((1 4,1 6,2 5,3 5,4 6,4 4,1 4)), ((4 2,4 3,6 3,6 2,4 2)))", 12, 7, 14.0);