diff --git a/finat/ufl/brokenelement.py b/finat/ufl/brokenelement.py
index 3e820288..2db1748e 100644
--- a/finat/ufl/brokenelement.py
+++ b/finat/ufl/brokenelement.py
@@ -10,11 +10,30 @@
 # Modified by Matthew Scroggs, 2023
 
 from finat.ufl.finiteelementbase import FiniteElementBase
+from finat.ufl.mixedelement import MixedElement, VectorElement, TensorElement
 from ufl.sobolevspace import L2
 
 
 class BrokenElement(FiniteElementBase):
     """The discontinuous version of an existing Finite Element space."""
+    def __new__(cls, element):
+        """
+        Broken qualifier must be below Mixed/Vector/Tensor so we
+        overload __new__ to return:
+
+        BrokenElement(MixedElement(elem0, elem1)) -> MixedElement(BrokenElement(elem0), BrokenElement(elem1))
+
+        and similarly for VectorElement and TensorElement.
+        """
+        if isinstance(element, (VectorElement, TensorElement)):
+            return element.reconstruct(sub_element=BrokenElement(element.sub_elements[0]))
+
+        elif isinstance(element, MixedElement):
+            return MixedElement(list(map(BrokenElement, element.sub_elements)))
+
+        else:  # hopefully no special casing needed
+            return super().__new__(cls)
+
     def __init__(self, element):
         """Init."""
         self._element = element
diff --git a/finat/ufl/mixedelement.py b/finat/ufl/mixedelement.py
index 20c25353..fb337812 100644
--- a/finat/ufl/mixedelement.py
+++ b/finat/ufl/mixedelement.py
@@ -345,9 +345,10 @@ def __repr__(self):
         """Doc."""
         return self._repr
 
-    def reconstruct(self, **kwargs):
+    def reconstruct(self, sub_element=None, **kwargs):
         """Doc."""
-        sub_element = self._sub_element.reconstruct(**kwargs)
+        if sub_element is None:
+            sub_element = self._sub_element.reconstruct(**kwargs)
         return VectorElement(sub_element, dim=len(self.sub_elements))
 
     def variant(self):
@@ -544,9 +545,10 @@ def symmetry(self):
         """
         return self._symmetry
 
-    def reconstruct(self, **kwargs):
+    def reconstruct(self, sub_element=None, **kwargs):
         """Doc."""
-        sub_element = self._sub_element.reconstruct(**kwargs)
+        if sub_element is None:
+            sub_element = self._sub_element.reconstruct(**kwargs)
         return TensorElement(sub_element, shape=self._shape, symmetry=self._symmetry)
 
     def __str__(self):
diff --git a/test/finat/test_create_broken_element.py b/test/finat/test_create_broken_element.py
new file mode 100644
index 00000000..6b6a04ed
--- /dev/null
+++ b/test/finat/test_create_broken_element.py
@@ -0,0 +1,49 @@
+import pytest
+import ufl
+from finat.ufl import FiniteElement, BrokenElement, VectorElement, TensorElement, MixedElement
+
+sub_elements = [
+    FiniteElement("CG", ufl.triangle, 1),
+    FiniteElement("BDM", ufl.triangle, 2),
+    FiniteElement("DG", ufl.interval, 2, variant="spectral")
+]
+
+sub_ids = [
+    "CG(1)",
+    "BDM(2)",
+    "DG(2,spectral)"
+]
+
+
+@pytest.mark.parametrize("sub_element", sub_elements, ids=sub_ids)
+@pytest.mark.parametrize("shape", (1, 2, (2, 3)), ids=("1", "2", "(2,3)"))
+def test_create_broken_vector_or_tensor_element(shape, sub_element):
+    """Check that BrokenElement returns a nested element
+    for mixed, vector, and tensor elements.
+    """
+    if not isinstance(shape, int):
+        make_element = lambda elem: TensorElement(elem, shape=shape)
+    else:
+        make_element = lambda elem: VectorElement(elem, dim=shape)
+
+    tensor = make_element(sub_element)
+    expected = make_element(BrokenElement(sub_element))
+
+    assert BrokenElement(tensor) == expected
+
+
+@pytest.mark.parametrize("sub_elements", [sub_elements, sub_elements[-1:]],
+                         ids=(f"nsubs={len(sub_elements)}", "nsubs=1"))
+def test_create_broken_mixed_element(sub_elements):
+    """Check that BrokenElement returns a nested element
+    for mixed, vector, and tensor elements.
+    """
+    mixed = MixedElement(sub_elements)
+    expected = MixedElement([BrokenElement(elem) for elem in sub_elements])
+    assert BrokenElement(mixed) == expected
+
+
+if __name__ == "__main__":
+    import os
+    import sys
+    pytest.main(args=[os.path.abspath(__file__)] + sys.argv[1:])