diff --git a/tests/firedrake/conftest.py b/tests/firedrake/conftest.py
index 80090a753c..f42b911b91 100644
--- a/tests/firedrake/conftest.py
+++ b/tests/firedrake/conftest.py
@@ -122,9 +122,13 @@ def pytest_collection_modifyitems(session, config, items):
 @pytest.fixture(scope="module", autouse=True)
 def check_empty_tape(request):
     """Check that the tape is empty at the end of each module"""
-    from pyadjoint.tape import get_working_tape
+    from pyadjoint.tape import annotate_tape, get_working_tape
 
     def fin():
+        # make sure taping is switched off
+        assert not annotate_tape()
+
+        # make sure the tape is empty
         tape = get_working_tape()
         if tape is not None:
             assert len(tape.get_blocks()) == 0
diff --git a/tests/firedrake/demos/test_demos_run.py b/tests/firedrake/demos/test_demos_run.py
index 9d6fdb9a3f..e08be26275 100644
--- a/tests/firedrake/demos/test_demos_run.py
+++ b/tests/firedrake/demos/test_demos_run.py
@@ -152,6 +152,7 @@ def test_serial_demo(demo, env, monkeypatch, tmpdir):
     _exec_file(py_file)
 
     if "adjoint" in demo.requirements:
+        pyadjoint.pause_annotation()
         pyadjoint.get_working_tape().clear_tape()
 
 
@@ -164,4 +165,5 @@ def test_parallel_demo(demo, env, monkeypatch, tmpdir):
     _exec_file(py_file)
 
     if "adjoint" in demo.requirements:
+        pyadjoint.pause_annotation()
         pyadjoint.get_working_tape().clear_tape()
diff --git a/tests/firedrake/regression/test_restricted_function_space.py b/tests/firedrake/regression/test_restricted_function_space.py
index 6dd093f58a..8d8a19a56d 100644
--- a/tests/firedrake/regression/test_restricted_function_space.py
+++ b/tests/firedrake/regression/test_restricted_function_space.py
@@ -358,7 +358,7 @@ def test_restricted_function_space_extrusion_stokes(ncells):
     sol_res = Function(W_res)
     solve(a_res == L_res, sol_res, bcs=[bc_res])
     # Compare.
-    assert assemble(inner(sol_res - sol, sol_res - sol) * dx)**0.5 < 1.e-15
+    assert assemble(inner(sol_res - sol, sol_res - sol) * dx)**0.5 < 1.e-14
     # -- Actually, the ordering is the same.
     assert np.allclose(sol_res.subfunctions[0].dat.data_ro_with_halos, sol.subfunctions[0].dat.data_ro_with_halos)
     assert np.allclose(sol_res.subfunctions[1].dat.data_ro_with_halos, sol.subfunctions[1].dat.data_ro_with_halos)