diff --git a/Lib/test/test_normalization.py b/Lib/test/test_normalization.py
index dbe1a11..b674371 100644
--- a/Lib/test/test_normalization.py
+++ b/Lib/test/test_normalization.py
@@ -54,9 +54,6 @@
             if line.startswith("@Part"):
                 part = line.split()[0]
                 continue
-            if part == "@Part3":
-                # XXX we don't support PRI #29 yet, so skip these tests for now
-                continue
             try:
                 c1,c2,c3,c4,c5 = [unistr(x) for x in line.split(';')[:-1]]
             except RangeError:
diff --git a/Lib/test/test_unicodedata.py b/Lib/test/test_unicodedata.py
index f8df2b6..0862c9b 100644
--- a/Lib/test/test_unicodedata.py
+++ b/Lib/test/test_unicodedata.py
@@ -188,9 +188,22 @@
 
     def test_pr29(self):
         # http://www.unicode.org/review/pr-29.html
-        for text in ("\u0b47\u0300\u0b3e", "\u1100\u0300\u1161"):
+        # See issues #1054943 and #10254.
+        composed = ("\u0b47\u0300\u0b3e", "\u1100\u0300\u1161",
+                    'Li\u030dt-s\u1e73\u0301',
+                    '\u092e\u093e\u0930\u094d\u0915 \u091c\u093c'
+                    + '\u0941\u0915\u0947\u0930\u092c\u0930\u094d\u0917',
+                    '\u0915\u093f\u0930\u094d\u0917\u093f\u091c\u093c'
+                    + '\u0938\u094d\u0924\u093e\u0928')
+        for text in composed:
             self.assertEqual(self.db.normalize('NFC', text), text)
 
+    def test_issue10254(self):
+        # Crash reported in #10254
+        a = 'C\u0338' * 20  + 'C\u0327'
+        b = 'C\u0338' * 20  + '\xC7'
+        self.assertEqual(self.db.normalize('NFC', a), b)
+
     def test_east_asian_width(self):
         eaw = self.db.east_asian_width
         self.assertRaises(TypeError, eaw, b'a')