diff --git a/tests/test_commonline_utils.py b/tests/test_commonline_utils.py
index bcced630a1..669d33ca01 100644
--- a/tests/test_commonline_utils.py
+++ b/tests/test_commonline_utils.py
@@ -98,8 +98,11 @@ def test_J_sync(dtype):
             Rijs_conjugated[ij] = Rij
             ij += 1
 
-    # Initialize JSync instance with default params.
-    J_sync = JSync(n)
+    # Initialize JSync instance.
+    # For this small problem, set epsilon to 1e-3 (default is 1e-2)
+    # to prevent premature power method stoppage due to residual
+    # dipping below epsilon on a single early iteration.
+    J_sync = JSync(n, epsilon=1e-3)
 
     # Perform power method and check that signs are correct up to
     # multilication by -1. Also check dtype pass-through.
diff --git a/tests/test_oriented_source.py b/tests/test_oriented_source.py
index 30bb080b9f..0fa10d6c8e 100644
--- a/tests/test_oriented_source.py
+++ b/tests/test_oriented_source.py
@@ -31,7 +31,7 @@ def src_fixture_id(params):
 @pytest.fixture(params=ESTIMATOR_SYMMETRY, ids=src_fixture_id)
 def src_fixture(request):
     estimator, symmetry = request.param
-    L = 8
+    L = 12  # Must be greater than 8 for Cn algos.
     n = 10
     vol = None
 
@@ -43,7 +43,7 @@ def src_fixture(request):
         estimator_kwargs.update({"n_theta": 36, "symmetry": symmetry})
 
     # Generate an origianl source and an oriented source.
-    og_src = Simulation(L=L, n=n, vols=vol, offsets=0)
+    og_src = Simulation(L=L, n=n, vols=vol, C=1, offsets=0, seed=0)
     orient_est = estimator(og_src, max_shift=1 / L, mask=False, **estimator_kwargs)
     oriented_src = OrientedSource(og_src, orient_est)
 
@@ -138,7 +138,7 @@ def test_save(src_fixture, save_mode):
     Test save function and save_mode.
     """
 
-    src = src_fixture[1]
+    src = src_fixture[1].cache()
 
     # Make a fresh tmp_dir
     with tempfile.TemporaryDirectory() as tmp_dir: