diff --git a/symfem/elements/kmv.py b/symfem/elements/kmv.py
index 9f8949ab..43a375f6 100644
--- a/symfem/elements/kmv.py
+++ b/symfem/elements/kmv.py
@@ -88,7 +88,7 @@ def __init__(self, reference: Reference, order: int):
                     )
                 poly = kmv_tri_polyset(1, 1)
 
-            elif order == 3:
+            elif order == 2:
                 for v_n, v in enumerate(reference.vertices):
                     dofs.append(
                         WeightedPointEvaluation(
@@ -115,7 +115,7 @@ def __init__(self, reference: Reference, order: int):
                 )
                 poly = kmv_tri_polyset(2, 3)
 
-            elif order == 4:
+            elif order == 3:
                 for v_n, v in enumerate(reference.vertices):
                     dofs.append(
                         WeightedPointEvaluation(
@@ -177,7 +177,7 @@ def __init__(self, reference: Reference, order: int):
                     )
                 poly = kmv_tet_polyset(1, 1, 1)
 
-            elif order == 4:
+            elif order == 2:
                 for v_n, v in enumerate(reference.vertices):
                     dofs.append(
                         WeightedPointEvaluation(
diff --git a/test/utils.py b/test/utils.py
index d303db3b..11054077 100644
--- a/test/utils.py
+++ b/test/utils.py
@@ -54,7 +54,7 @@
         "BDFM": [({"variant": "equispaced"}, range(1, 4))],
         "Argyris": [({}, [5])],
         "MTW": [({"variant": "equispaced"}, [3])],
-        "KMV": [({}, [1, 3])],
+        "KMV": [({}, [1, 2])],
         "Hermite": [({}, [3])],
         "BDM": [({"variant": "equispaced"}, range(1, 4))],
         "Bernstein": [({}, range(1, 4))],