diff --git a/Lib/pathlib.py b/Lib/pathlib.py
--- a/Lib/pathlib.py
+++ b/Lib/pathlib.py
@@ -749,17 +749,19 @@
         """Return a new path with the file name changed."""
         if not self.name:
             raise ValueError("%r has an empty name" % (self,))
+        drv, root, parts = self._flavour.parse_parts((name,))
+        if (not name or name[-1] in [self._flavour.sep, self._flavour.altsep] or
+            drv or root or len(parts) != 1):
+            raise ValueError("Invalid name %r" % (name))
         return self._from_parsed_parts(self._drv, self._root,
                                        self._parts[:-1] + [name])
 
     def with_suffix(self, suffix):
         """Return a new path with the file suffix changed (or added, if none)."""
         # XXX if suffix is None, should the current suffix be removed?
-        drv, root, parts = self._flavour.parse_parts((suffix,))
-        if drv or root or len(parts) != 1:
-            raise ValueError("Invalid suffix %r" % (suffix))
-        suffix = parts[0]
-        if not suffix.startswith('.'):
+        if (self._flavour.sep in suffix or
+            self._flavour.altsep and self._flavour.altsep in suffix or
+            suffix and not suffix.startswith('.') or suffix == '.'):
             raise ValueError("Invalid suffix %r" % (suffix))
         name = self.name
         if not name:
diff --git a/Lib/test/test_pathlib.py b/Lib/test/test_pathlib.py
--- a/Lib/test/test_pathlib.py
+++ b/Lib/test/test_pathlib.py
@@ -540,6 +540,10 @@
         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, '/c')
+        self.assertRaises(ValueError, P('a/b').with_name, 'c/')
+        self.assertRaises(ValueError, P('a/b').with_name, 'c/d')
 
     def test_with_suffix_common(self):
         P = self.cls
@@ -547,6 +551,9 @@
         self.assertEqual(P('/a/b').with_suffix('.gz'), P('/a/b.gz'))
         self.assertEqual(P('a/b.py').with_suffix('.gz'), P('a/b.gz'))
         self.assertEqual(P('/a/b.py').with_suffix('.gz'), P('/a/b.gz'))
+        # Stripping suffix
+        self.assertEqual(P('a/b.py').with_suffix(''), P('a/b'))
+        self.assertEqual(P('/a/b').with_suffix(''), P('/a/b'))
         # Path doesn't have a "filename" component
         self.assertRaises(ValueError, P('').with_suffix, '.gz')
         self.assertRaises(ValueError, P('.').with_suffix, '.gz')
@@ -554,9 +561,13 @@
         # Invalid suffix
         self.assertRaises(ValueError, P('a/b').with_suffix, 'gz')
         self.assertRaises(ValueError, P('a/b').with_suffix, '/')
+        self.assertRaises(ValueError, P('a/b').with_suffix, '.')
         self.assertRaises(ValueError, P('a/b').with_suffix, '/.gz')
+        self.assertRaises(ValueError, P('a/b').with_suffix, '.gz/')
         self.assertRaises(ValueError, P('a/b').with_suffix, 'c/d')
         self.assertRaises(ValueError, P('a/b').with_suffix, '.c/.d')
+        self.assertRaises(ValueError, P('a/b').with_suffix, './.d')
+        self.assertRaises(ValueError, P('a/b').with_suffix, '.d/.')
 
     def test_relative_to_common(self):
         P = self.cls
@@ -950,6 +961,9 @@
         self.assertRaises(ValueError, P('c:').with_name, 'd.xml')
         self.assertRaises(ValueError, P('c:/').with_name, 'd.xml')
         self.assertRaises(ValueError, P('//My/Share').with_name, 'd.xml')
+        self.assertRaises(ValueError, P('c:a/b').with_name, 'd:')
+        self.assertRaises(ValueError, P('c:a/b').with_name, 'd:e')
+        self.assertRaises(ValueError, P('c:a/b').with_name, 'd:/e')
 
     def test_with_suffix(self):
         P = self.cls