diff --git a/Lib/copy_reg.py b/Lib/copy_reg.py
index db17150..8943077 100644
--- a/Lib/copy_reg.py
+++ b/Lib/copy_reg.py
@@ -127,7 +127,11 @@
                         continue
                     # mangled names
                     elif name.startswith('__') and not name.endswith('__'):
-                        names.append('_%s%s' % (c.__name__, name))
+                        stripped = c.__name__.lstrip('_')
+                        if stripped:
+                            names.append('_%s%s' % (stripped, name))
+                        else:
+                            names.append(name)
                     else:
                         names.append(name)
 
diff --git a/Lib/test/test_copy_reg.py b/Lib/test/test_copy_reg.py
index 8cdb8b7..17ccbd0 100644
--- a/Lib/test/test_copy_reg.py
+++ b/Lib/test/test_copy_reg.py
@@ -17,6 +17,12 @@
 class WithPrivate(object):
     __slots__ = ('__spam',)
 
+class _WithLeadingUnderscoreAndPrivate(object):
+    __slots__ = ('__spam',)
+
+class ___(object):
+    __slots__ = ('__spam',)
+
 class WithSingleString(object):
     __slots__ = 'spam'
 
@@ -105,6 +111,10 @@
         self.assertEqual(copy_reg._slotnames(WithWeakref), [])
         expected = ['_WithPrivate__spam']
         self.assertEqual(copy_reg._slotnames(WithPrivate), expected)
+        expected = ['_WithLeadingUnderscoreAndPrivate__spam']
+        self.assertEqual(copy_reg._slotnames(_WithLeadingUnderscoreAndPrivate),
+                         expected)
+        self.assertEqual(copy_reg._slotnames(___), ['__spam'])
         self.assertEqual(copy_reg._slotnames(WithSingleString), ['spam'])
         expected = ['eggs', 'spam']
         expected.sort()
diff --git a/Misc/ACKS b/Misc/ACKS
index 662db9f..229a874 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -543,6 +543,7 @@
 Brian Harring
 Jonathan Hartley
 Travis B. Hartwell
+Shane Harvey
 Larry Hastings
 Tim Hatch
 Shane Hathaway
diff --git a/Misc/NEWS.d/next/Library/2017-08-02-12-48-15.bpo-31107.1t2hn5.rst b/Misc/NEWS.d/next/Library/2017-08-02-12-48-15.bpo-31107.1t2hn5.rst
new file mode 100644
index 0000000..0980705
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-08-02-12-48-15.bpo-31107.1t2hn5.rst
@@ -0,0 +1,2 @@
+Fix `copy_reg._slotnames()` mangled attribute calculation for classes whose
+name begins with an underscore. Patch by Shane Harvey.