diff --git a/tests/test_updater.py b/tests/test_updater.py
index 9cc06e1b..a181b412 100644
--- a/tests/test_updater.py
+++ b/tests/test_updater.py
@@ -1845,7 +1845,7 @@ def test_get_one_valid_targetinfo(self):
         multi_repo_updater.get_one_valid_targetinfo, 'non-existent.txt')
     multi_repo_updater.map_file['mapping'][1]['terminating'] = True
 
-    # Test for a mapping that sets terminating = True, and that occurs before
+    # Test for a mapping that sets terminating = True, and that appears before
     # the final mapping.
     multi_repo_updater.map_file['mapping'][0]['terminating'] = True
     self.assertRaises(tuf.exceptions.UnknownTargetError,
diff --git a/tuf/client/updater.py b/tuf/client/updater.py
index 8b2a8d09..ec954848 100755
--- a/tuf/client/updater.py
+++ b/tuf/client/updater.py
@@ -342,7 +342,7 @@ def get_one_valid_targetinfo(self, target_filename):
 
       else:
         logger.debug('The mapping was irrelevant to the targets, and'
-            ' "terminating" was set to False.'
+            ' "terminating" was set to False.')
 
     # If we are here, it means either there were no mappings, or none of the
     # mappings provided the target.
diff --git a/tuf/formats.py b/tuf/formats.py
index 056031f2..08ffcefa 100755
--- a/tuf/formats.py
+++ b/tuf/formats.py
@@ -268,7 +268,7 @@
 # A Dict containing the map file's "mapping" attribute.
 MAPPING_SCHEMA = SCHEMA.ListOf(SCHEMA.Object(
   paths = RELPATHS_SCHEMA,
-  repositories = REPO_NAMES_TO_MIRRORS_SCHEMA,
+  repositories = SCHEMA.ListOf(securesystemslib.formats.URL_SCHEMA),
   terminating = BOOLEAN_SCHEMA,
   threshold = THRESHOLD_SCHEMA))