diff --git a/spacy/displacy/render.py b/spacy/displacy/render.py
index 8d39e62f5..247ad996b 100644
--- a/spacy/displacy/render.py
+++ b/spacy/displacy/render.py
@@ -397,6 +397,7 @@ class DependencyRenderer:
         args (list): Individual arcs and their start, end, direction and label.
         RETURNS (dict): Arc levels keyed by (start, end, label).
         """
+        arcs = [dict(t) for t in {tuple(sorted(arc.items())) for arc in arcs}]
         length = max([arc["end"] for arc in arcs], default=0)
         max_level = [0] * length
         levels = {}
diff --git a/spacy/tests/test_displacy.py b/spacy/tests/test_displacy.py
index 95dc47a19..f52c36889 100644
--- a/spacy/tests/test_displacy.py
+++ b/spacy/tests/test_displacy.py
@@ -8,26 +8,6 @@ from spacy.lang.fa import Persian
 from spacy.tokens import Span, Doc
 
 
-@pytest.mark.issue(5447)
-def test_issue5447():
-    """Test that overlapping arcs get separate levels."""
-    renderer = DependencyRenderer()
-    words = [
-        {"text": "This", "tag": "DT"},
-        {"text": "is", "tag": "VBZ"},
-        {"text": "a", "tag": "DT"},
-        {"text": "sentence.", "tag": "NN"},
-    ]
-    arcs = [
-        {"start": 0, "end": 1, "label": "nsubj", "dir": "left"},
-        {"start": 2, "end": 3, "label": "det", "dir": "left"},
-        {"start": 2, "end": 3, "label": "overlap", "dir": "left"},
-        {"start": 1, "end": 3, "label": "attr", "dir": "left"},
-    ]
-    html = renderer.render([{"words": words, "arcs": arcs}])
-    assert renderer.highest_level == 3
-
-
 @pytest.mark.issue(2361)
 def test_issue2361(de_vocab):
     """Test if < is escaped when rendering"""
@@ -103,6 +83,27 @@ def test_issue3882(en_vocab):
     displacy.parse_deps(doc)
 
 
+@pytest.mark.issue(5447)
+def test_issue5447():
+    """Test that overlapping arcs get separate levels, unless they're identical."""
+    renderer = DependencyRenderer()
+    words = [
+        {"text": "This", "tag": "DT"},
+        {"text": "is", "tag": "VBZ"},
+        {"text": "a", "tag": "DT"},
+        {"text": "sentence.", "tag": "NN"},
+    ]
+    arcs = [
+        {"start": 0, "end": 1, "label": "nsubj", "dir": "left"},
+        {"start": 2, "end": 3, "label": "det", "dir": "left"},
+        {"start": 2, "end": 3, "label": "overlap", "dir": "left"},
+        {"end": 3, "label": "overlap", "start": 2, "dir": "left"},
+        {"start": 1, "end": 3, "label": "attr", "dir": "left"},
+    ]
+    renderer.render([{"words": words, "arcs": arcs}])
+    assert renderer.highest_level == 3
+
+
 @pytest.mark.issue(5838)
 def test_issue5838():
     # Displacy's EntityRenderer break line