diff --git a/firedrake/trefftz.py b/firedrake/trefftz.py
index dae0e94ebb..aa40759fb8 100644
--- a/firedrake/trefftz.py
+++ b/firedrake/trefftz.py
@@ -17,11 +17,21 @@
 class TrefftzEmbedding(object):
     """
     This class computes the Trefftz embedding of a given function space
-    :arg V: the function space
-    :arg b: the bilinear form defining the embedding
-    :arg dim: the dimension of the embedding
-    :arg tol: the tolerance for the singular values
-    :arg backend: the backend to use for the computation of the SVD
+    Parameters
+    ----------
+    V : :class:`.FunctionSpace`
+        Ambient function space.
+    b : :class:`.ufl.form.Form`
+        Bilinear form defining the Trefftz operator.
+    dim : int, optional
+        Dimension of the embedding.
+        Default is the dimension of the function space.
+    tol : float, optional
+        Tolerance for the singular values cutoff.
+        Default is 1e-12.
+    backend : str, optional
+        Backend to use for the computation of the SVD.
+        Default is "scipy".
     """
     def __init__(self, V, b, dim=None, tol=1e-12, backend="scipy"):
         self.V = V
@@ -60,6 +70,10 @@ def __init__(self):
     def get_appctx(ksp):
         """
         Get the application context from the KSP
+        Parameters
+        ----------
+        ksp : :class:`PETSc.KSP`
+            The KSP object
         """
         from firedrake.dmhooks import get_appctx
         return get_appctx(ksp.getDM()).appctx
@@ -67,6 +81,10 @@ def get_appctx(ksp):
     def setUp(self, ksp):
         """
         Set up the Trefftz KSP
+        Parameters
+        ----------
+        ksp : :class:`PETSc.KSP`
+            The KSP object
         """
         appctx = self.get_appctx(ksp)
         self.QT, _ = appctx["trefftz_embedding"].assemble()
@@ -74,6 +92,14 @@ def setUp(self, ksp):
     def solve(self, ksp, b, x):
         """
         Solve the Trefftz KSP
+        Parameters
+        ----------
+        ksp : :class:`PETSc.KSP`
+            The KSP object
+        b : :class:`PETSc.Vec`
+            The right-hand side
+        x : :class:`PETSc.Vec`
+            The solution
         """
         A, P = ksp.getOperators()
         self.Q = PETSc.Mat().createTranspose(self.QT)
@@ -95,11 +121,20 @@ def solve(self, ksp, b, x):
 class AggregationEmbedding(TrefftzEmbedding):
     """
     This class computes the aggregation embedding of a given function space.
-    :arg V: the function space
-    :arg mesh: the mesh
-    :arg polyMesh: the aggregation mesh
-    :arg dim: the dimension of the embedding
-    :arg tol: the tolerance for the singular values
+    Parameters
+    ----------
+    V : :class:`.FunctionSpace`
+        Ambient function space.
+    mesh : :class:`.Mesh`
+        The mesh on which the aggregation is defined.
+    polyMesh : :class:`.Function`
+        The function defining the aggregation.
+    dim : int
+        Dimension of the embedding.
+        Default is the dimension of the function space.
+    tol : float
+        Tolerance for the singular values cutoff.
+        Default is 1e-12.
     """
     def __init__(self, V, mesh, polyMesh, dim=None, tol=1e-12):
         # Relabel facets that are inside an aggregated region
@@ -139,9 +174,14 @@ def __init__(self, V, mesh, polyMesh, dim=None, tol=1e-12):
 def jump_normal(u, n, k):
     """
     Compute the jump of the normal derivative of a function u
-    :arg u: the function
-    :arg n: the normal vector
-    :arg k: the degree of the normal derivative
+    Parameters
+    ----------
+    u : :class:`.Function`
+        The function.
+    n : :class:`.ufc.Normal`
+        The normal vector.
+    k : int
+        The order of the normal derivative we aim to compute.
     """
     j = 0.5*dot(n, (grad(u)("+")-grad(u)("-")))
     for _ in range(1, k):
@@ -152,7 +192,10 @@ def jump_normal(u, n, k):
 def dumb_aggregation(mesh):
     """
     Compute a dumb aggregation of the mesh
-    :arg mesh: the mesh
+    Parameters
+    ----------
+    mesh : :class:`.Mesh`
+        The mesh we aim to aggregate.
     """
     if mesh.comm.size > 1:
         raise NotImplementedError("Parallel mesh aggregation not supported")
diff --git a/tests/regression/test_trefftz.py b/tests/regression/test_trefftz.py
index bbbe6823cf..c23566be08 100644
--- a/tests/regression/test_trefftz.py
+++ b/tests/regression/test_trefftz.py
@@ -1,6 +1,7 @@
 from firedrake import *
 from firedrake.trefftz import TrefftzEmbedding, AggregationEmbedding, dumb_aggregation
 
+
 @pytest.mark.skipcomplex
 def test_trefftz_laplace():
     order = 6
@@ -38,6 +39,7 @@ def delta(u):
     assert (assemble(inner(uDG-f, uDG-f)*dx) < 1e-6)
     assert (embd.dimT < V.dim()/2)
 
+
 @pytest.mark.skipcomplex
 def test_trefftz_aggregation():
     from netgen.occ import WorkPlane, OCCGeometry