python
diff --git a/Doc/c-api/module.rst b/Doc/c-api/module.rst
@@ -264,7 +264,7 @@ of the following two module creation functions:
       instead; only use this if you are sure you need it.
 
 Before it is returned from in the initialization function, the resulting module
-object is typically populated using functions like :c:func:`PyModule_AddObject`.
+object is typically populated using functions like :c:func:`PyModule_AddObjectRef`.
 
 .. _multi-phase-initialization:
 
@@ -437,26 +437,102 @@ a function called from a module execution slot (if using multi-phase
 initialization), can use the following functions to help initialize the module
 state:
 
+.. c:function:: int PyModule_AddObjectRef(PyObject *module, const char *name, PyObject *value)
+
+   Add an object to *module* as *name*.  This is a convenience function which
+   can be used from the module's initialization function.
+
+   On success, return ``0``. On error, raise an exception and return ``-1``.
+
+   Return ``NULL`` if *value* is ``NULL``. It must be called with an exception
+   raised in this case.
+
+   Example usage::
+
+       static int
+       add_spam(PyObject *module, int value)
+       {
+           PyObject *obj = PyLong_FromLong(value);
+           if (obj == NULL) {
+               return -1;
+           }
+           int res = PyModule_AddObjectRef(module, "spam", obj);
+           Py_DECREF(obj);
+           return res;
+        }
+
+   The example can also be written without checking explicitly if *obj* is
+   ``NULL``::
+
+       static int
+       add_spam(PyObject *module, int value)
+       {
+           PyObject *obj = PyLong_FromLong(value);
+           int res = PyModule_AddObjectRef(module, "spam", obj);
+           Py_XDECREF(obj);
+           return res;
+        }
+
+   Note that ``Py_XDECREF()`` should be used instead of ``Py_DECREF()`` in
+   this case, since *obj* can be ``NULL``.
+
+   .. versionadded:: 3.10
+
+
 .. c:function:: int PyModule_AddObject(PyObject *module, const char *name, PyObject *value)
 
-   Add an object to *module* as *name*.  This is a convenience function which can
-   be used from the module's initialization function.  This steals a reference to
-   *value* on success. Return ``-1`` on error, ``0`` on success.
+   Similar to :c:func:`PyModule_AddObjectRef`, but steals a reference to
+   *value* on success (if it returns ``0``).
+
+   The new :c:func:`PyModule_AddObjectRef` function is recommended, since it is
+   easy to introduce reference leaks by misusing the
+   :c:func:`PyModule_AddObject` function.
 
    .. note::
 
-      Unlike other functions that steal references, ``PyModule_AddObject()`` only
-      decrements the reference count of *value* **on success**.
+      Unlike other functions that steal references, ``PyModule_AddObject()``
+      only decrements the reference count of *value* **on success**.
 
       This means that its return value must be checked, and calling code must
-      :c:func:`Py_DECREF` *value* manually on error. Example usage::
-
-         Py_INCREF(spam);
-         if (PyModule_AddObject(module, "spam", spam) < 0) {
-             Py_DECREF(module);
-             Py_DECREF(spam);
-             return NULL;
-         }
+      :c:func:`Py_DECREF` *value* manually on error.
+
+   Example usage::
+
+      static int
+      add_spam(PyObject *module, int value)
+      {
+          PyObject *obj = PyLong_FromLong(value);
+          if (obj == NULL) {
+              return -1;
+          }
+          if (PyModule_AddObject(module, "spam", obj) < 0) {
+              Py_DECREF(obj);
+              return -1;
+          }
+          // PyModule_AddObject() stole a reference to obj:
+          // Py_DECREF(obj) is not needed here
+          return 0;
+      }
+
+   The example can also be written without checking explicitly if *obj* is
+   ``NULL``::
+
+      static int
+      add_spam(PyObject *module, int value)
+      {
+          PyObject *obj = PyLong_FromLong(value);
+          if (PyModule_AddObject(module, "spam", obj) < 0) {
+              Py_XDECREF(obj);
+              return -1;
+          }
+          // PyModule_AddObject() stole a reference to obj:
+          // Py_DECREF(obj) is not needed here
+          return 0;
+      }
+
+   Note that ``Py_XDECREF()`` should be used instead of ``Py_DECREF()`` in
+   this case, since *obj* can be ``NULL``.
+
 
 .. c:function:: int PyModule_AddIntConstant(PyObject *module, const char *name, long value)
 

diff --git a/Doc/whatsnew/3.10.rst b/Doc/whatsnew/3.10.rst
@@ -366,6 +366,11 @@ New Features
 * Added :c:func:`PyUnicode_AsUTF8AndSize` to the limited C API.
   (Contributed by Alex Gaynor in :issue:`41784`.)
 
+* Added :c:func:`PyModule_AddObjectRef` function: similar to
+  :c:func:`PyModule_AddObjectRef` but don't steal a reference to the value on
+  success.
+  (Contributed by Victor Stinner in :issue:`1635741`.)
+
 
 Porting to Python 3.10
 ----------------------

diff --git a/Include/modsupport.h b/Include/modsupport.h
@@ -136,7 +136,15 @@ PyAPI_FUNC(PyObject * const *) _PyArg_UnpackKeywords(
 void _PyArg_Fini(void);
 #endif   /* Py_LIMITED_API */
 
-PyAPI_FUNC(int) PyModule_AddObject(PyObject *, const char *, PyObject *);
+// Add an attribute with name 'name' and value 'obj' to the module 'mod.
+// On success, return 0 on success.
+// On error, raise an exception and return -1.
+PyAPI_FUNC(int) PyModule_AddObjectRef(PyObject *mod, const char *name, PyObject *value);
+
+// Similar to PyModule_AddObjectRef() but steal a reference to 'obj'
+// (Py_DECREF(obj)) on success (if it returns 0).
+PyAPI_FUNC(int) PyModule_AddObject(PyObject *mod, const char *, PyObject *value);
+
 PyAPI_FUNC(int) PyModule_AddIntConstant(PyObject *, const char *, long);
 PyAPI_FUNC(int) PyModule_AddStringConstant(PyObject *, const char *, const char *);
 #if !defined(Py_LIMITED_API) || Py_LIMITED_API+0 >= 0x03090000

diff --git a/Misc/NEWS.d/next/C API/2020-11-03-11-52-27.bpo-1635741.aDYJKB.rst b/Misc/NEWS.d/next/C API/2020-11-03-11-52-27.bpo-1635741.aDYJKB.rst
@@ -0,0 +1,3 @@
+Added :c:func:`PyModule_AddObjectRef` function: similar to
+:c:func:`PyModule_AddObjectRef` but don't steal a reference to the value on
+success. Patch by Victor Stinner.
diff --git a/Python/modsupport.c b/Python/modsupport.c
@@ -634,56 +634,70 @@ va_build_stack(PyObject **small_stack, Py_ssize_t small_stack_len,
 
 
 int
-PyModule_AddObject(PyObject *m, const char *name, PyObject *o)
+PyModule_AddObjectRef(PyObject *mod, const char *name, PyObject *value)
 {
-    PyObject *dict;
-    if (!PyModule_Check(m)) {
+    if (!PyModule_Check(mod)) {
         PyErr_SetString(PyExc_TypeError,
-                    "PyModule_AddObject() needs module as first arg");
+                        "PyModule_AddObjectRef() first argument "
+                        "must be a module");
         return -1;
     }
-    if (!o) {
-        if (!PyErr_Occurred())
-            PyErr_SetString(PyExc_TypeError,
-                            "PyModule_AddObject() needs non-NULL value");
+    if (!value) {
+        if (!PyErr_Occurred()) {
+            PyErr_SetString(PyExc_SystemError,
+                            "PyModule_AddObjectRef() must be called "
+                            "with an exception raised if value is NULL");
+        }
         return -1;
     }
 
-    dict = PyModule_GetDict(m);
+    PyObject *dict = PyModule_GetDict(mod);
     if (dict == NULL) {
         /* Internal error -- modules must have a dict! */
         PyErr_Format(PyExc_SystemError, "module '%s' has no __dict__",
-                     PyModule_GetName(m));
+                     PyModule_GetName(mod));
         return -1;
     }
-    if (PyDict_SetItemString(dict, name, o))
+
+    if (PyDict_SetItemString(dict, name, value)) {
         return -1;
-    Py_DECREF(o);
+    }
     return 0;
 }
 
+
+int
+PyModule_AddObject(PyObject *mod, const char *name, PyObject *value)
+{
+    int res = PyModule_AddObjectRef(mod, name, value);
+    if (res == 0) {
+        Py_DECREF(value);
+    }
+    return res;
+}
+
 int
 PyModule_AddIntConstant(PyObject *m, const char *name, long value)
 {
-    PyObject *o = PyLong_FromLong(value);
-    if (!o)
+    PyObject *obj = PyLong_FromLong(value);
+    if (!obj) {
         return -1;
-    if (PyModule_AddObject(m, name, o) == 0)
-        return 0;
-    Py_DECREF(o);
-    return -1;
+    }
+    int res = PyModule_AddObjectRef(m, name, obj);
+    Py_DECREF(obj);
+    return res;
 }
 
 int
 PyModule_AddStringConstant(PyObject *m, const char *name, const char *value)
 {
-    PyObject *o = PyUnicode_FromString(value);
-    if (!o)
+    PyObject *obj = PyUnicode_FromString(value);
+    if (!obj) {
         return -1;
-    if (PyModule_AddObject(m, name, o) == 0)
-        return 0;
-    Py_DECREF(o);
-    return -1;
+    }
+    int res = PyModule_AddObjectRef(m, name, obj);
+    Py_DECREF(obj);
+    return res;
 }
 
 int
@@ -696,11 +710,5 @@ PyModule_AddType(PyObject *module, PyTypeObject *type)
     const char *name = _PyType_Name(type);
     assert(name != NULL);
 
-    Py_INCREF(type);
-    if (PyModule_AddObject(module, name, (PyObject *)type) < 0) {
-        Py_DECREF(type);
-        return -1;
-    }
-
-    return 0;
+    return PyModule_AddObjectRef(module, name, (PyObject *)type);
 }