diff --git a/docs/source/element_list.py b/docs/source/element_list.py
index 4671bfcf1b..b55094be16 100644
--- a/docs/source/element_list.py
+++ b/docs/source/element_list.py
@@ -1,5 +1,8 @@
 from finat.ufl.elementlist import ufl_elements
-from finat.element_factory import supported_elements
+from finat.element_factory import supported_elements, create_element
+from finat.ufl import FiniteElement
+from ufl.cell import TensorProductCell
+from ufl import interval, quadrilateral
 import csv
 
 shape_names = {
@@ -8,17 +11,15 @@
     2: 'tensor'
     }
 
-def cells(cellnames):
+firedrake_cells = ("interval",
+                    "triangle",
+                    "tetrahedron",
+                    "quadrilateral",
+                    "hexahedron")
 
-    firedrake_cells = ("interval",
-                       "triangle",
-                       "tetrahedron",
-                       "quadrilateral",
-                       "hexahedron")
 
-    cells = [c for c in cellnames if c in firedrake_cells]
-
-    return(", ".join(cells))
+def cells(cell_list):
+    return(", ".join(cell_list))
 
 
 with open("element_list.csv", 'w', newline='') as csvfile:
@@ -26,10 +27,30 @@ def cells(cellnames):
 
     for element in supported_elements:
         family, short_name, value_rank, sobolev_space, \
-            mapping, degree_range, cellnames = ufl_elements[element]
+            mapping, degree_range, cell_list = ufl_elements[element]
 
+        cell_list = [c for c in cell_list if c in firedrake_cells]
         short_name = short_name if short_name != family else ""
-        cellnames = cells(cellnames)
+        cellnames = cells(cell_list)
         shape = shape_names[value_rank]
 
-        csvwriter.writerow((family, short_name, shape, cellnames))
+        if family in {"Q", "DQ", "DQ L2"}:
+            cell = cell_list[-1]
+        elif family in {"NCE", "NCF"}:
+            cell = TensorProductCell(quadrilateral, interval)
+        else:
+            cell = cell_list[0]
+
+        ufl_elem = FiniteElement(family, cell=cell, degree=degree_range[0])
+        finat_element = create_element(ufl_elem)
+
+        if short_name in {"BDMCF", "BDMCE"}:
+            interpolatable = "No"
+        else:
+            try:
+                finat_element.dual_basis
+                interpolatable = "Yes"
+            except NotImplementedError:
+                interpolatable = "No"
+
+        csvwriter.writerow((family, short_name, shape, cellnames, interpolatable))
diff --git a/docs/source/variational-problems.rst b/docs/source/variational-problems.rst
index e164f6c620..3d02a51441 100644
--- a/docs/source/variational-problems.rst
+++ b/docs/source/variational-problems.rst
@@ -267,11 +267,12 @@ extrusion <extruded-meshes>` for details.
 Supported finite elements
 -------------------------
 
-Firedrake supports the use of the following finite elements.
+Firedrake supports the use of the following finite elements. The last column
+specifies if we support interpolation **into** a function space built from the element.
 
 .. csv-table::
-    :header: "Name", "Short name", "Value shape", "Valid cells"
-    :widths: 20, 10, 10, 40
+    :header: "Name", "Short name", "Value shape", "Valid cells", "Supports interpolation?"
+    :widths: 20, 10, 10, 40, 10
     :file: element_list.csv
 
 In addition, the
diff --git a/pyproject.toml b/pyproject.toml
index 1f3a7f92cc..0feff1cb55 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -23,7 +23,7 @@ dependencies = [
   # TODO RELEASE
   "fenics-ufl @ git+https://github.com/FEniCS/ufl.git@main",
   # TODO RELEASE
-  "firedrake-fiat @ git+https://github.com/firedrakeproject/fiat.git@main",
+  "firedrake-fiat @ git+https://github.com/firedrakeproject/fiat.git@leo/misc-fixes",
   "h5py>3.12.1",
   "immutabledict",
   "libsupermesh",