diff --git a/pyerrors/obs.py b/pyerrors/obs.py
index a806c597..6889fd3f 100644
--- a/pyerrors/obs.py
+++ b/pyerrors/obs.py
@@ -1356,7 +1356,7 @@ def covariance(obs, visualize=False, correlation=False, **kwargs):
     length = len(obs)
 
     max_samples = np.max([o.N for o in obs])
-    if max_samples <= length:
+    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
         warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
 
     cov = np.zeros((length, length))
diff --git a/tests/obs_test.py b/tests/obs_test.py
index 3d773951..a2f40fdf 100644
--- a/tests/obs_test.py
+++ b/tests/obs_test.py
@@ -696,6 +696,15 @@ def test_covariance_correlation():
     assert np.allclose(pe.covariance([test_obs, test_obs, test_obs], correlation=True), np.ones((3, 3)))
 
 
+def test_covariance_rank_deficient():
+    obs = []
+    for i in range(5):
+        obs.append(pe.pseudo_Obs(1.0, 0.1, 'test', 5))
+
+    with pytest.warns(RuntimeWarning):
+        pe.covariance(obs)
+
+
 def test_empty_obs():
     o = pe.Obs([np.random.rand(100)], ['test'])
     q = o + pe.Obs([], [])