diff --git a/CHANGES.rst b/CHANGES.rst
index 45da96a44..d5fb9b8d1 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,6 +1,14 @@
 Traits CHANGELOG
 ================
 
+Upcoming release X.Y.Z
+----------------------
+
+Removals
+~~~~~~~~
+* Make ``NoDefaultSpecified`` private and remove it from the public API.(#1380)
+
+
 Release 6.1.1
 -------------
 
diff --git a/docs/source/traits_api_reference/trait_type.rst b/docs/source/traits_api_reference/trait_type.rst
index ac04c8134..73b55cf5b 100644
--- a/docs/source/traits_api_reference/trait_type.rst
+++ b/docs/source/traits_api_reference/trait_type.rst
@@ -7,8 +7,6 @@
 Classes
 -------
 
-.. autoclass:: NoDefaultSpecified
-
 .. autoclass:: TraitType
 
 Private Functions
diff --git a/traits-stubs/traits-stubs/trait_type.pyi b/traits-stubs/traits-stubs/trait_type.pyi
index b5ae8b312..ec9a5201b 100644
--- a/traits-stubs/traits-stubs/trait_type.pyi
+++ b/traits-stubs/traits-stubs/trait_type.pyi
@@ -14,11 +14,6 @@ from .base_trait_handler import BaseTraitHandler as BaseTraitHandler
 
 trait_types: Dict[str, int]
 
-
-class NoDefaultSpecified:
-    ...
-
-
 _Accepts = TypeVar('_Accepts')
 
 _Stores = TypeVar('_Stores')
diff --git a/traits/tests/test_readonly.py b/traits/tests/test_readonly.py
new file mode 100644
index 000000000..aa5dd4103
--- /dev/null
+++ b/traits/tests/test_readonly.py
@@ -0,0 +1,48 @@
+# (C) Copyright 2005-2021 Enthought, Inc., Austin, TX
+# All rights reserved.
+#
+# This software is provided without warranty under the terms of the BSD
+# license included in LICENSE.txt and may be redistributed only under
+# the conditions described in the aforementioned license. The license
+# is also available online at http://www.enthought.com/licenses/BSD.txt
+#
+# Thanks for using Enthought open source!
+
+"""
+Tests for the ReadOnly trait type.
+
+"""
+import unittest
+
+from traits.api import (
+    HasTraits,
+    ReadOnly,
+    TraitError,
+)
+
+
+class ObjectWithReadOnlyText(HasTraits):
+    """ A dummy object that set the readonly trait in __init__
+
+    There exists such usage in TraitsUI.
+    """
+
+    text = ReadOnly()
+
+    def __init__(self, text, **traits):
+        self.text = text
+        super(ObjectWithReadOnlyText, self).__init__(**traits)
+
+
+class TestReadOnlyTrait(unittest.TestCase):
+    """ Test ReadOnly TraitType. """
+
+    def test_set_readonly_trait_in_init(self):
+
+        obj = ObjectWithReadOnlyText(text="ABC")
+        self.assertEqual(obj.text, "ABC")
+
+        with self.assertRaises(TraitError):
+            obj.text = "XYZ"
+
+        self.assertEqual(obj.text, "ABC")
diff --git a/traits/trait_type.py b/traits/trait_type.py
index 88403d3ee..7757590ab 100644
--- a/traits/trait_type.py
+++ b/traits/trait_type.py
@@ -69,11 +69,11 @@ def _read_only(object, name, value):
 
 
 # Create a singleton object for use in the TraitType constructor:
-class NoDefaultSpecified(object):
+class _NoDefaultSpecified(object):
     pass
 
 
-no_default_specified = NoDefaultSpecified()
+_no_default_specified = _NoDefaultSpecified()
 
 
 class TraitType(BaseTraitHandler):
@@ -173,7 +173,7 @@ class TraitType(BaseTraitHandler):
     #: The metadata for the trait.
     metadata = {}
 
-    def __init__(self, default_value=no_default_specified, **metadata):
+    def __init__(self, default_value=_no_default_specified, **metadata):
         """ TraitType initializer
 
         This is the only method normally called directly by client code.
@@ -183,7 +183,7 @@ def __init__(self, default_value=no_default_specified, **metadata):
         Override this method whenever a different method signature or a
         validated default value is needed.
         """
-        if default_value is not no_default_specified:
+        if default_value is not _no_default_specified:
             self.default_value = default_value
 
         if len(metadata) > 0:
@@ -257,7 +257,7 @@ def get_default_value(self):
 
         return (dvt, dv)
 
-    def clone(self, default_value=no_default_specified, **metadata):
+    def clone(self, default_value=_no_default_specified, **metadata):
         """ Copy, optionally modifying default value and metadata.
 
         Clones the contents of this object into a new instance of the same
@@ -294,7 +294,7 @@ def clone(self, default_value=no_default_specified, **metadata):
 
         new._metadata.update(metadata)
 
-        if default_value is not no_default_specified:
+        if default_value is not _no_default_specified:
             new.default_value = default_value
             if self.validate is not None:
                 try: