diff --git a/certbot/renewal.py b/certbot/renewal.py
index 23dbe191b..6678d0247 100644
--- a/certbot/renewal.py
+++ b/certbot/renewal.py
@@ -32,6 +32,8 @@ INT_CONFIG_ITEMS = ["rsa_key_size", "tls_sni_01_port", "http01_port"]
 STR_CONFIG_ITEMS = ["config_dir", "logs_dir", "work_dir", "user_agent",
                     "server", "account", "authenticator", "installer",
                     "standalone_supported_challenges", "renew_hook"]
+CONFIG_ITEMS = set(itertools.chain(
+    BOOL_CONFIG_ITEMS, INT_CONFIG_ITEMS, STR_CONFIG_ITEMS))
 
 
 def _reconstitute(config, full_path):
diff --git a/certbot/storage.py b/certbot/storage.py
index e4fc21a85..4095ba862 100644
--- a/certbot/storage.py
+++ b/certbot/storage.py
@@ -183,9 +183,8 @@ def _relevant(option):
     from certbot import renewal
     from certbot.plugins import disco as plugins_disco
     plugins = list(plugins_disco.PluginsRegistry.find_all())
-    return (option in renewal.STR_CONFIG_ITEMS
-            or option in renewal.INT_CONFIG_ITEMS
-            or any(option.startswith(x + "_") for x in plugins))
+    return (option in renewal.CONFIG_ITEMS or
+            any(option.startswith(x + "_") for x in plugins))
 
 
 def relevant_values(all_values):
diff --git a/certbot/tests/storage_test.py b/certbot/tests/storage_test.py
index a1fda6535..f52f31d3d 100644
--- a/certbot/tests/storage_test.py
+++ b/certbot/tests/storage_test.py
@@ -551,7 +551,8 @@ class RenewableCertTests(BaseRenewableCertTest):
 
         from certbot.storage import relevant_values
         with mock.patch("certbot.cli.helpful_parser", mock_parser):
-            return relevant_values(values)
+            # make a copy to ensure values isn't modified
+            return relevant_values(values.copy())
 
     def test_relevant_values(self):
         """Test that relevant_values() can reject an irrelevant value."""
@@ -567,10 +568,18 @@ class RenewableCertTests(BaseRenewableCertTest):
     def test_relevant_values_nondefault(self):
         """Test that relevant_values() can retain a non-default value."""
         values = {"rsa_key_size": 12}
-        # A copy is given to _test_relevant_values_common
-        # to make sure values isn't modified by the method
         self.assertEqual(
-            self._test_relevant_values_common(values.copy()), values)
+            self._test_relevant_values_common(values), values)
+
+    def test_relevant_values_bool(self):
+        values = {"allow_subset_of_names": True}
+        self.assertEqual(
+            self._test_relevant_values_common(values), values)
+
+    def test_relevant_values_str(self):
+        values = {"authenticator": "apache"}
+        self.assertEqual(
+            self._test_relevant_values_common(values), values)
 
     @mock.patch("certbot.storage.relevant_values")
     def test_new_lineage(self, mock_rv):