diff --git a/tests/test_core.py b/tests/test_core.py
index ddf08ea..95aeab4 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -2,6 +2,7 @@
 
 from numpy.testing import assert_raises
 
+from jax_cosmo import Configuration
 from jax_cosmo import Cosmology
 
 
@@ -21,6 +22,13 @@ def test_Cosmology_immutability():
         cosmo.h = 0.74  # Hubble doesn't budge on the tension
 
 
+def test_Conguration_immutability():
+    config = Configuration()
+
+    with assert_raises(FrozenInstanceError):
+        config.log10_a_max = 0.0
+
+
 def test_cache():
     cosmo = Cosmology(
         Omega_c=0.25,
@@ -33,21 +41,22 @@ def test_cache():
         wa=0.0,
     )
 
+    def assert_pure(c1, c2):
+        assert c1 is not c2 and c1 == c2 and c1._cache != c2._cache
+
     cosmo = cosmo.cache_set("a", 1)
     cosmo = cosmo.cache_set("c", 3)
+
     assert cosmo.is_cached("a")
     assert not cosmo.is_cached("b")
     assert cosmo.cache_get("c") == 3
 
-    cosmo = cosmo.cache_set("b", 2)
-    cosmo_no_c = cosmo.cache_del("c")
-    assert cosmo.is_cached("b")
-    assert not cosmo_no_c.is_cached("c")
-    assert (
-        cosmo_no_c is not cosmo
-        and cosmo_no_c == cosmo
-        and cosmo_no_c._cache != cosmo._cache
-    )
+    cosmo_add_b = cosmo.cache_set("b", 2)
+    cosmo_del_c = cosmo.cache_del("c")
+    cosmo_clean = cosmo.cache_clear()
 
-    cosmo = cosmo.cache_clear()
-    assert len(cosmo._cache) == 0
+    assert not cosmo_del_c.is_cached("c")
+    assert_pure(cosmo_add_b, cosmo)  # test set purity
+    assert_pure(cosmo_del_c, cosmo)  # test del purity
+    assert_pure(cosmo_clean, cosmo)  # test clear purity
+    assert len(cosmo_clean._cache) == 0