Index: Objects/unicodectype.c
===================================================================
--- Objects/unicodectype.c	(revision 71863)
+++ Objects/unicodectype.c	(working copy)
@@ -87,7 +87,7 @@
 	delta = ctype->upper;
 
     if (ctype->flags & NODELTA_MASK)
-	return delta;
+	return delta ? delta : ch;
 
     if (delta >= 32768)
 	    delta -= 65536;
@@ -772,7 +772,7 @@
     const _PyUnicode_TypeRecord *ctype = gettyperecord(ch);
     int delta = ctype->upper;
     if (ctype->flags & NODELTA_MASK)
-	return delta;
+	return delta ? delta : ch;
     if (delta >= 32768)
 	    delta -= 65536;
     return ch + delta;
@@ -786,7 +786,7 @@
     const _PyUnicode_TypeRecord *ctype = gettyperecord(ch);
     int delta = ctype->lower;
     if (ctype->flags & NODELTA_MASK)
-	return delta;
+	return delta ? delta : ch;
     if (delta >= 32768)
 	    delta -= 65536;
     return ch + delta;
Index: Lib/test/test_unicodedata.py
===================================================================
--- Lib/test/test_unicodedata.py	(revision 71863)
+++ Lib/test/test_unicodedata.py	(working copy)
@@ -20,7 +20,7 @@
 class UnicodeMethodsTest(unittest.TestCase):
 
     # update this, if the database changes
-    expectedchecksum = 'aef99984a58c8e1e5363a3175f2ff9608599a93e'
+    expectedchecksum = 'b7db9b5f1d804976fa921d2009cbef6f025620c1'
 
     def test_method_checksum(self):
         h = hashlib.sha1()
@@ -258,7 +258,19 @@
         # the upper-case mapping: as delta, or as absolute value
         self.assert_("a".upper()=='A')
         self.assert_("\u1d79".upper()=='\ua77d')
+        self.assert_(".".upper()=='.')
 
+    def test_bug_5828(self):
+        self.assertEqual("\u1d79".lower(), "\u1d79")
+        # Only U+0000 should have U+0000 as its upper/lower/titlecase variant
+        self.assertEqual(
+            [
+                c for c in range(sys.maxunicode+1)
+                if chr(c).lower() == "\x00" or chr(c).upper() == "\x00" or chr(c).title() == "\x00"
+            ],
+            [0]
+        )
+
 def test_main():
     test.support.run_unittest(
         UnicodeMiscTest,