diff --git a/Lib/test/test_pathlib/test_pathlib_abc.py b/Lib/test/test_pathlib/test_pathlib_abc.py
index 3a7c036077e2a1..0b886d0a91765d 100644
--- a/Lib/test/test_pathlib/test_pathlib_abc.py
+++ b/Lib/test/test_pathlib/test_pathlib_abc.py
@@ -212,10 +212,13 @@ def test_eq_common(self):
         self.assertNotEqual(P(), {})
         self.assertNotEqual(P(), int)
 
-    def test_match_common(self):
+    def test_match_empty(self):
         P = self.cls
         self.assertRaises(ValueError, P('a').match, '')
         self.assertRaises(ValueError, P('a').match, '.')
+
+    def test_match_common(self):
+        P = self.cls
         # Simple relative pattern.
         self.assertTrue(P('b.py').match('b.py'))
         self.assertTrue(P('a/b.py').match('b.py'))
@@ -395,14 +398,17 @@ def test_anchor_common(self):
         self.assertEqual(P('/').anchor, sep)
         self.assertEqual(P('/a/b').anchor, sep)
 
-    def test_name_common(self):
+    def test_name_empty(self):
         P = self.cls
         self.assertEqual(P('').name, '')
         self.assertEqual(P('.').name, '')
+        self.assertEqual(P('/a/b/.').name, 'b')
+
+    def test_name_common(self):
+        P = self.cls
         self.assertEqual(P('/').name, '')
         self.assertEqual(P('a/b').name, 'b')
         self.assertEqual(P('/a/b').name, 'b')
-        self.assertEqual(P('/a/b/.').name, 'b')
         self.assertEqual(P('a/b.py').name, 'b.py')
         self.assertEqual(P('/a/b.py').name, 'b.py')
 
@@ -445,10 +451,13 @@ def test_suffixes_common(self):
         self.assertEqual(P('a/Some name. Ending with a dot.').suffixes, [])
         self.assertEqual(P('/a/Some name. Ending with a dot.').suffixes, [])
 
-    def test_stem_common(self):
+    def test_stem_empty(self):
         P = self.cls
         self.assertEqual(P('').stem, '')
         self.assertEqual(P('.').stem, '')
+
+    def test_stem_common(self):
+        P = self.cls
         self.assertEqual(P('..').stem, '..')
         self.assertEqual(P('/').stem, '')
         self.assertEqual(P('a/b').stem, 'b')
@@ -467,11 +476,17 @@ def test_with_name_common(self):
         self.assertEqual(P('/a/b.py').with_name('d.xml'), P('/a/d.xml'))
         self.assertEqual(P('a/Dot ending.').with_name('d.xml'), P('a/d.xml'))
         self.assertEqual(P('/a/Dot ending.').with_name('d.xml'), P('/a/d.xml'))
+
+    def test_with_name_empty(self):
+        P = self.cls
         self.assertRaises(ValueError, P('').with_name, 'd.xml')
         self.assertRaises(ValueError, P('.').with_name, 'd.xml')
         self.assertRaises(ValueError, P('/').with_name, 'd.xml')
         self.assertRaises(ValueError, P('a/b').with_name, '')
         self.assertRaises(ValueError, P('a/b').with_name, '.')
+
+    def test_with_name_seps(self):
+        P = self.cls
         self.assertRaises(ValueError, P('a/b').with_name, '/c')
         self.assertRaises(ValueError, P('a/b').with_name, 'c/')
         self.assertRaises(ValueError, P('a/b').with_name, 'c/d')
@@ -485,11 +500,17 @@ def test_with_stem_common(self):
         self.assertEqual(P('/a/b.tar.gz').with_stem('d'), P('/a/d.gz'))
         self.assertEqual(P('a/Dot ending.').with_stem('d'), P('a/d'))
         self.assertEqual(P('/a/Dot ending.').with_stem('d'), P('/a/d'))
+
+    def test_with_stem_empty(self):
+        P = self.cls
         self.assertRaises(ValueError, P('').with_stem, 'd')
         self.assertRaises(ValueError, P('.').with_stem, 'd')
         self.assertRaises(ValueError, P('/').with_stem, 'd')
         self.assertRaises(ValueError, P('a/b').with_stem, '')
         self.assertRaises(ValueError, P('a/b').with_stem, '.')
+
+    def test_with_stem_seps(self):
+        P = self.cls
         self.assertRaises(ValueError, P('a/b').with_stem, '/c')
         self.assertRaises(ValueError, P('a/b').with_stem, 'c/')
         self.assertRaises(ValueError, P('a/b').with_stem, 'c/d')
@@ -503,10 +524,16 @@ def test_with_suffix_common(self):
         # Stripping suffix.
         self.assertEqual(P('a/b.py').with_suffix(''), P('a/b'))
         self.assertEqual(P('/a/b').with_suffix(''), P('/a/b'))
+
+    def test_with_suffix_empty(self):
+        P = self.cls
         # Path doesn't have a "filename" component.
         self.assertRaises(ValueError, P('').with_suffix, '.gz')
         self.assertRaises(ValueError, P('.').with_suffix, '.gz')
         self.assertRaises(ValueError, P('/').with_suffix, '.gz')
+
+    def test_with_suffix_seps(self):
+        P = self.cls
         # Invalid suffix.
         self.assertRaises(ValueError, P('a/b').with_suffix, 'gz')
         self.assertRaises(ValueError, P('a/b').with_suffix, '/')