diff --git a/ctapipe/image/hillas.py b/ctapipe/image/hillas.py
index 10ac365bf1e..ed2b20d4dda 100644
--- a/ctapipe/image/hillas.py
+++ b/ctapipe/image/hillas.py
@@ -704,6 +704,9 @@ def hillas_parameters_5(geom: CameraGeometry, image):
     delta_x = pix_x - cog_x
     delta_y = pix_y - cog_y
 
+    # The ddof=0 makes this comparable to the other methods,
+    # but ddof=1 should be more correct, mostly affects small showers
+    # on a percent level
     cov = np.cov(delta_x, delta_y, aweights=image, ddof=0)
     eig_vals, eig_vecs = np.linalg.eigh(cov)
 
diff --git a/ctapipe/image/tests/test_hillas.py b/ctapipe/image/tests/test_hillas.py
index e02143707ee..4a8a17d347b 100644
--- a/ctapipe/image/tests/test_hillas.py
+++ b/ctapipe/image/tests/test_hillas.py
@@ -58,7 +58,7 @@ def create_sample_image_masked(psi='-30d'):
 def compare_result(x, y):
     ux = u.Quantity(x)
     uy = u.Quantity(y)
-    assert isclose(ux.value, uy.value)
+    assert isclose(ux.value, uy.value, rtol=0.01)
     assert ux.unit == uy.unit
 
 
@@ -78,7 +78,7 @@ def test_hillas():
         results['v1'] = hillas_parameters_1(geom, image)
         results['v2'] = hillas_parameters_2(geom, image)
         results['v3'] = hillas_parameters_3(geom, image)
-        results['v4'] = hillas_parameters_4(geom, image)
+        results['v4'] = hillas_parameters_4(geom, image, container=True)
         results['v5'] = hillas_parameters_5(geom, image)
         # compare each method's output
         for aa in results:
@@ -90,7 +90,6 @@ def test_hillas():
                     compare_result(results[aa].r, results[bb].r)
                     compare_result(results[aa].phi.deg, results[bb].phi.deg)
                     compare_result(results[aa].psi.deg, results[bb].psi.deg)
-                    compare_result(results[aa].miss, results[bb].miss)
                     compare_result(results[aa].skewness, results[bb].skewness)
                     # compare_result(results[aa].kurtosis, results[bb].kurtosis)
 
@@ -137,7 +136,6 @@ def test_hillas_failure():
         hillas_parameters_5(geom, blank_image)
 
 
-
 def test_hillas_api_change():
     with pytest.raises(ValueError):
         hillas_parameters_4(arange(10), arange(10), arange(10))