diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
index 48e5095..dddf0f8 100644
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -2508,11 +2508,17 @@
 
         # Check that an invalid tzname result raises an exception.
         class Badtzname(tzinfo):
-            def tzname(self, dt): return 42
+            tz = 42
+            def tzname(self, dt): return self.tz
         t = time(2, 3, 4, tzinfo=Badtzname())
         self.assertEqual(t.strftime("%H:%M:%S"), "02:03:04")
         self.assertRaises(TypeError, t.strftime, "%Z")
 
+        # Issue #6697:
+        if '_Fast' in str(type(self)):
+            Badtzname.tz = '\ud800'
+            self.assertRaises(ValueError, t.strftime, "%Z")
+
     def test_hash_edge_cases(self):
         # Offsets that overflow a basic time.
         t1 = self.theclass(0, 1, 2, 3, tzinfo=FixedOffset(1439, ""))
diff --git a/Lib/test/test_pyexpat.py b/Lib/test/test_pyexpat.py
index 5a193bb..5bb8c97 100644
--- a/Lib/test/test_pyexpat.py
+++ b/Lib/test/test_pyexpat.py
@@ -203,6 +203,8 @@
 
         operations = out.out
         self._verify_parse_output(operations)
+        # Issue #6697.
+        self.assertRaises(AttributeError, getattr, parser, '\uD800')
 
     def test_parse_file(self):
         # Try parsing a file
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 32084da..6bdb6c9 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -667,6 +667,8 @@
                                type=socket.SOCK_STREAM, proto=0,
                                flags=socket.AI_PASSIVE)
         self.assertEqual(a, b)
+        # Issue #6697.
+        self.assertRaises(UnicodeEncodeError, socket.getaddrinfo, 'localhost', '\uD800')
 
     def test_getnameinfo(self):
         # only IP addresses are allowed
diff --git a/Lib/test/test_syslog.py b/Lib/test/test_syslog.py
index 028dcb4..4e7621e 100644
--- a/Lib/test/test_syslog.py
+++ b/Lib/test/test_syslog.py
@@ -11,6 +11,8 @@
 
     def test_openlog(self):
         syslog.openlog('python')
+        # Issue #6697.
+        self.assertRaises(UnicodeEncodeError, syslog.openlog, '\uD800')
 
     def test_syslog(self):
         syslog.openlog('python')
diff --git a/Lib/test/test_xml_etree_c.py b/Lib/test/test_xml_etree_c.py
index ee270f9..5c0bf6c 100644
--- a/Lib/test/test_xml_etree_c.py
+++ b/Lib/test/test_xml_etree_c.py
@@ -8,10 +8,26 @@
 # cElementTree specific tests
 
 def sanity():
-    """
+    r"""
     Import sanity.
 
     >>> from xml.etree import cElementTree
+
+    Issue #6697.
+
+    >>> e = cElementTree.Element('a')
+    >>> getattr(e, '\uD800')           # doctest: +ELLIPSIS
+    Traceback (most recent call last):
+      ...
+    UnicodeEncodeError: ...
+
+    >>> p = cElementTree.XMLParser()
+    >>> p.version.split()[0]
+    'Expat'
+    >>> getattr(p, '\uD800')
+    Traceback (most recent call last):
+     ...
+    AttributeError: 'XMLParser' object has no attribute '\ud800'
     """