diff --git a/CHANGES b/CHANGES
index cdd8475b49..2e6a9a6237 100644
--- a/CHANGES
+++ b/CHANGES
@@ -17,6 +17,9 @@ Features added
 * #7888: napoleon: Add aliases Warn and Raise.
 * C, added :rst:dir:`c:alias` directive for inserting copies
   of existing declarations.
+* #7052: add ``:noindexentry:`` to the Python, C, C++, and Javascript domains.
+  Update the documentation to better reflect the relationship between this option
+  and the ``:noindex:`` option.
 
 Bugs fixed
 ----------
diff --git a/doc/usage/restructuredtext/domains.rst b/doc/usage/restructuredtext/domains.rst
index 285e5b826f..311b03d666 100644
--- a/doc/usage/restructuredtext/domains.rst
+++ b/doc/usage/restructuredtext/domains.rst
@@ -42,9 +42,22 @@ Basic Markup
 Most domains provide a number of :dfn:`object description directives`, used to
 describe specific objects provided by modules.  Each directive requires one or
 more signatures to provide basic information about what is being described, and
-the content should be the description.  The basic version makes entries in the
-general index; if no index entry is desired, you can give the directive option
-flag ``:noindex:``.  An example using a Python domain directive::
+the content should be the description.  A domain will typically keep an
+internal index of all entites to aid cross-referencing. Typically it will
+also add entries in the shown general index.
+If you want to suppress the addition of an entry in the shown index, you can
+give the directive option flag ``:noindexentry:``.
+If you want to typeset an object description, without even making it available
+for cross-referencing, you can give the directive option flag ``:noindex:``
+(which implies ``:noindexentry:``).
+Though, note that not every directive en every domain may support these
+options.
+
+.. versionadded:: 3.2
+   The directive option ``noindexentry`` in the Python, C, C++, and Javascript
+   domains.
+
+An example using a Python domain directive::
 
    .. py:function:: spam(eggs)
                     ham(eggs)
@@ -1073,6 +1086,7 @@ Options
 
 Some directives support options:
 
+- ``:noindexentry:``, see :ref:`basic-domain-markup`.
 - ``:tparam-line-spec:``, for templated declarations.
   If specified, each template parameter will be rendered on a separate line.
 
diff --git a/sphinx/domains/c.py b/sphinx/domains/c.py
index 8a0b8a1054..10ced026d3 100644
--- a/sphinx/domains/c.py
+++ b/sphinx/domains/c.py
@@ -16,6 +16,7 @@ from typing import cast
 
 from docutils import nodes
 from docutils.nodes import Element, Node, TextElement, system_message
+from docutils.parsers.rst import directives
 
 from sphinx import addnodes
 from sphinx.addnodes import pending_xref
@@ -3023,10 +3024,7 @@ class CObject(ObjectDescription):
     ]
 
     option_spec = {
-        # have a dummy option to ensure proper errors on options,
-        # otherwise the option is taken as a continuation of the
-        # argument
-        'dummy': None
+        'noindexentry': directives.flag,
     }
 
     def _add_enumerator_to_parent(self, ast: ASTDeclaration) -> None:
@@ -3098,8 +3096,9 @@ class CObject(ObjectDescription):
             if name not in domain.objects:
                 domain.objects[name] = (domain.env.docname, newestId, self.objtype)
 
-        indexText = self.get_index_text(name)
-        self.indexnode['entries'].append(('single', indexText, newestId, '', None))
+        if 'noindexentry' not in self.options:
+            indexText = self.get_index_text(name)
+            self.indexnode['entries'].append(('single', indexText, newestId, '', None))
 
     @property
     def object_type(self) -> str:
diff --git a/sphinx/domains/cpp.py b/sphinx/domains/cpp.py
index 310691d495..c840423aad 100644
--- a/sphinx/domains/cpp.py
+++ b/sphinx/domains/cpp.py
@@ -6625,6 +6625,7 @@ class CPPObject(ObjectDescription):
     ]
 
     option_spec = {
+        'noindexentry': directives.flag,
         'tparam-line-spec': directives.flag,
     }
 
@@ -6701,7 +6702,7 @@ class CPPObject(ObjectDescription):
             if decl.objectType == 'concept':
                 isInConcept = True
                 break
-        if not isInConcept:
+        if not isInConcept and 'noindexentry' not in self.options:
             strippedName = name
             for prefix in self.env.config.cpp_index_common_prefix:
                 if name.startswith(prefix):
diff --git a/sphinx/domains/javascript.py b/sphinx/domains/javascript.py
index d510d79034..6c75f8dd79 100644
--- a/sphinx/domains/javascript.py
+++ b/sphinx/domains/javascript.py
@@ -49,6 +49,11 @@ class JSObject(ObjectDescription):
     #: based on directive nesting
     allow_nesting = False
 
+    option_spec = {
+        'noindex': directives.flag,
+        'noindexentry': directives.flag,
+    }
+
     def handle_signature(self, sig: str, signode: desc_signature) -> Tuple[str, str]:
         """Breaks down construct signatures
 
@@ -120,9 +125,10 @@ class JSObject(ObjectDescription):
         domain = cast(JavaScriptDomain, self.env.get_domain('js'))
         domain.note_object(fullname, self.objtype, node_id, location=signode)
 
-        indextext = self.get_index_text(mod_name, name_obj)
-        if indextext:
-            self.indexnode['entries'].append(('single', indextext, node_id, '', None))
+        if 'noindexentry' not in self.options:
+            indextext = self.get_index_text(mod_name, name_obj)
+            if indextext:
+                self.indexnode['entries'].append(('single', indextext, node_id, '', None))
 
     def get_index_text(self, objectname: str, name_obj: Tuple[str, str]) -> str:
         name, obj = name_obj
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 5ea8d5d3da..4ca6062484 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -317,6 +317,7 @@ class PyObject(ObjectDescription):
     """
     option_spec = {
         'noindex': directives.flag,
+        'noindexentry': directives.flag,
         'module': directives.unchanged,
         'annotation': directives.unchanged,
     }
@@ -459,9 +460,10 @@ class PyObject(ObjectDescription):
         domain = cast(PythonDomain, self.env.get_domain('py'))
         domain.note_object(fullname, self.objtype, node_id, location=signode)
 
-        indextext = self.get_index_text(modname, name_cls)
-        if indextext:
-            self.indexnode['entries'].append(('single', indextext, node_id, '', None))
+        if 'noindexentry' not in self.options:
+            indextext = self.get_index_text(modname, name_cls)
+            if indextext:
+                self.indexnode['entries'].append(('single', indextext, node_id, '', None))
 
     def before_content(self) -> None:
         """Handle object nesting before content
@@ -576,16 +578,17 @@ class PyFunction(PyObject):
     def add_target_and_index(self, name_cls: Tuple[str, str], sig: str,
                              signode: desc_signature) -> None:
         super().add_target_and_index(name_cls, sig, signode)
-        modname = self.options.get('module', self.env.ref_context.get('py:module'))
-        node_id = signode['ids'][0]
+        if 'noindexentry' not in self.options:
+            modname = self.options.get('module', self.env.ref_context.get('py:module'))
+            node_id = signode['ids'][0]
 
-        name, cls = name_cls
-        if modname:
-            text = _('%s() (in module %s)') % (name, modname)
-            self.indexnode['entries'].append(('single', text, node_id, '', None))
-        else:
-            text = '%s; %s()' % (pairindextypes['builtin'], name)
-            self.indexnode['entries'].append(('pair', text, node_id, '', None))
+            name, cls = name_cls
+            if modname:
+                text = _('%s() (in module %s)') % (name, modname)
+                self.indexnode['entries'].append(('single', text, node_id, '', None))
+            else:
+                text = '%s; %s()' % (pairindextypes['builtin'], name)
+                self.indexnode['entries'].append(('pair', text, node_id, '', None))
 
     def get_index_text(self, modname: str, name_cls: Tuple[str, str]) -> str:
         # add index in own add_target_and_index() instead.
diff --git a/tests/test_domain_c.py b/tests/test_domain_c.py
index 347f8c7d6a..efef104f95 100644
--- a/tests/test_domain_c.py
+++ b/tests/test_domain_c.py
@@ -10,6 +10,7 @@
 import pytest
 
 from sphinx import addnodes
+from sphinx.addnodes import desc
 from sphinx.domains.c import DefinitionParser, DefinitionError
 from sphinx.domains.c import _max_id, _id_prefix, Symbol
 from sphinx.testing import restructuredtext
@@ -590,3 +591,13 @@ def test_cvar(app):
     domain = app.env.get_domain('c')
     entry = domain.objects.get('PyClass_Type')
     assert entry == ('index', 'c.PyClass_Type', 'var')
+
+
+def test_noindexentry(app):
+    text = (".. c:function:: void f()\n"
+            ".. c:function:: void g()\n"
+            "   :noindexentry:\n")
+    doctree = restructuredtext.parse(app, text)
+    assert_node(doctree, (addnodes.index, desc, addnodes.index, desc))
+    assert_node(doctree[0], addnodes.index, entries=[('single', 'f (C function)', 'c.f', '', None)])
+    assert_node(doctree[2], addnodes.index, entries=[])
diff --git a/tests/test_domain_cpp.py b/tests/test_domain_cpp.py
index a6c9eee9d1..28e437219a 100644
--- a/tests/test_domain_cpp.py
+++ b/tests/test_domain_cpp.py
@@ -14,8 +14,11 @@ import pytest
 
 import sphinx.domains.cpp as cppDomain
 from sphinx import addnodes
+from sphinx.addnodes import desc
 from sphinx.domains.cpp import DefinitionParser, DefinitionError, NoOldIdError
 from sphinx.domains.cpp import Symbol, _max_id, _id_prefix
+from sphinx.testing import restructuredtext
+from sphinx.testing.util import assert_node
 from sphinx.util import docutils
 
 
@@ -1211,3 +1214,13 @@ not found in `{test}`
     assert any_role.classes == cpp_any_role.classes, expect
     assert any_role.classes == expr_role.content_classes['a'], expect
     assert any_role.classes == texpr_role.content_classes['a'], expect
+
+
+def test_noindexentry(app):
+    text = (".. cpp:function:: void f()\n"
+            ".. cpp:function:: void g()\n"
+            "   :noindexentry:\n")
+    doctree = restructuredtext.parse(app, text)
+    assert_node(doctree, (addnodes.index, desc, addnodes.index, desc))
+    assert_node(doctree[0], addnodes.index, entries=[('single', 'f (C++ function)', '_CPPv41fv', '', None)])
+    assert_node(doctree[2], addnodes.index, entries=[])
diff --git a/tests/test_domain_js.py b/tests/test_domain_js.py
index 189f22e5b4..9d0b59b919 100644
--- a/tests/test_domain_js.py
+++ b/tests/test_domain_js.py
@@ -218,3 +218,13 @@ def test_js_data(app):
     assert_node(doctree[0], addnodes.index,
                 entries=[("single", "name (global variable or constant)", "name", "", None)])
     assert_node(doctree[1], addnodes.desc, domain="js", objtype="data", noindex=False)
+
+
+def test_noindexentry(app):
+    text = (".. js:function:: f()\n"
+            ".. js:function:: g()\n"
+            "   :noindexentry:\n")
+    doctree = restructuredtext.parse(app, text)
+    assert_node(doctree, (addnodes.index, desc, addnodes.index, desc))
+    assert_node(doctree[0], addnodes.index, entries=[('single', 'f() (built-in function)', 'f', '', None)])
+    assert_node(doctree[2], addnodes.index, entries=[])
diff --git a/tests/test_domain_py.py b/tests/test_domain_py.py
index 25d9ae7dff..61cc5145b6 100644
--- a/tests/test_domain_py.py
+++ b/tests/test_domain_py.py
@@ -799,3 +799,19 @@ def test_modindex_common_prefix(app):
     )
 
 
+def test_noindexentry(app):
+    text = (".. py:function:: f()\n"
+            ".. py:function:: g()\n"
+            "   :noindexentry:\n")
+    doctree = restructuredtext.parse(app, text)
+    assert_node(doctree, (addnodes.index, desc, addnodes.index, desc))
+    assert_node(doctree[0], addnodes.index, entries=[('pair', 'built-in function; f()', 'f', '', None)])
+    assert_node(doctree[2], addnodes.index, entries=[])
+
+    text = (".. py:class:: f\n"
+            ".. py:class:: g\n"
+            "   :noindexentry:\n")
+    doctree = restructuredtext.parse(app, text)
+    assert_node(doctree, (addnodes.index, desc, addnodes.index, desc))
+    assert_node(doctree[0], addnodes.index, entries=[('single', 'f (built-in class)', 'f', '', None)])
+    assert_node(doctree[2], addnodes.index, entries=[])