diff --git a/Doc/c-api/module.rst b/Doc/c-api/module.rst
index 68cbda2..feca1ec 100644
--- a/Doc/c-api/module.rst
+++ b/Doc/c-api/module.rst
@@ -417,7 +417,22 @@
 
    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*.  Return ``-1`` on error, ``0`` on success.
+   *value* on success.  Return ``-1`` on error, ``0`` on success.
+
+   .. note::
+
+      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:function:: int PyModule_AddIntConstant(PyObject *module, const char *name, long value)
 
diff --git a/Doc/extending/extending.rst b/Doc/extending/extending.rst
index e459514..5b4ea82 100644
--- a/Doc/extending/extending.rst
+++ b/Doc/extending/extending.rst
@@ -209,7 +209,7 @@
    static PyObject *SpamError;
 
 and initialize it in your module's initialization function (:c:func:`PyInit_spam`)
-with an exception object (leaving out the error checking for now)::
+with an exception object::
 
    PyMODINIT_FUNC
    PyInit_spam(void)
@@ -221,8 +221,14 @@
            return NULL;
 
        SpamError = PyErr_NewException("spam.error", NULL, NULL);
-       Py_INCREF(SpamError);
-       PyModule_AddObject(m, "error", SpamError);
+       Py_XINCREF(SpamError);
+       if (PyModule_AddObject(m, "error", SpamError) < 0) {
+           Py_XDECREF(SpamError);
+           Py_CLEAR(SpamError);
+           Py_DECREF(m);
+           return NULL;
+       }
+
        return m;
    }
 
@@ -1261,8 +1267,12 @@
        /* Create a Capsule containing the API pointer array's address */
        c_api_object = PyCapsule_New((void *)PySpam_API, "spam._C_API", NULL);
 
-       if (c_api_object != NULL)
-           PyModule_AddObject(m, "_C_API", c_api_object);
+       if (PyModule_AddObject(m, "_C_API", c_api_object) < 0) {
+           Py_XDECREF(c_api_object);
+           Py_DECREF(m);
+           return NULL;
+       }
+
        return m;
    }
 
diff --git a/Doc/extending/newtypes_tutorial.rst b/Doc/extending/newtypes_tutorial.rst
index 59c8cc0..94ca747 100644
--- a/Doc/extending/newtypes_tutorial.rst
+++ b/Doc/extending/newtypes_tutorial.rst
@@ -179,7 +179,12 @@
 to the appropriate default values, including :attr:`ob_type` that we initially
 set to *NULL*. ::
 
-   PyModule_AddObject(m, "Custom", (PyObject *) &CustomType);
+   Py_INCREF(&CustomType);
+   if (PyModule_AddObject(m, "Custom", (PyObject *) &CustomType) < 0) {
+       Py_DECREF(&CustomType);
+       PY_DECREF(m);
+       return NULL;
+   }
 
 This adds the type to the module dictionary.  This allows us to create
 :class:`Custom` instances by calling the :class:`Custom` class:
@@ -864,7 +869,12 @@
            return NULL;
 
        Py_INCREF(&SubListType);
-       PyModule_AddObject(m, "SubList", (PyObject *) &SubListType);
+       if (PyModule_AddObject(m, "SubList", (PyObject *) &SubListType) < 0) {
+           Py_DECREF(&SubListType);
+           Py_DECREF(m);
+           return NULL;
+       }
+
        return m;
    }
 
diff --git a/Doc/includes/custom.c b/Doc/includes/custom.c
index 13d16f5..bda32e2 100644
--- a/Doc/includes/custom.c
+++ b/Doc/includes/custom.c
@@ -35,6 +35,11 @@
         return NULL;
 
     Py_INCREF(&CustomType);
-    PyModule_AddObject(m, "Custom", (PyObject *) &CustomType);
+    if (PyModule_AddObject(m, "Custom", (PyObject *) &CustomType) < 0) {
+        Py_DECREF(&CustomType);
+        PY_DECREF(m);
+        return NULL;
+    }
+
     return m;
 }
diff --git a/Doc/includes/custom2.c b/Doc/includes/custom2.c
index 6477a19..5bacab7 100644
--- a/Doc/includes/custom2.c
+++ b/Doc/includes/custom2.c
@@ -128,6 +128,11 @@
         return NULL;
 
     Py_INCREF(&CustomType);
-    PyModule_AddObject(m, "Custom", (PyObject *) &CustomType);
+    if (PyModule_AddObject(m, "Custom", (PyObject *) &CustomType) < 0) {
+        Py_DECREF(&CustomType);
+        Py_DECREF(m);
+        return NULL;
+    }
+
     return m;
 }
diff --git a/Doc/includes/custom3.c b/Doc/includes/custom3.c
index 213d086..2b7a99e 100644
--- a/Doc/includes/custom3.c
+++ b/Doc/includes/custom3.c
@@ -179,6 +179,11 @@
         return NULL;
 
     Py_INCREF(&CustomType);
-    PyModule_AddObject(m, "Custom", (PyObject *) &CustomType);
+    if (PyModule_AddObject(m, "Custom", (PyObject *) &CustomType) < 0) {
+        Py_DECREF(&CustomType);
+        Py_DECREF(m);
+        return NULL;
+    }
+
     return m;
 }
diff --git a/Doc/includes/custom4.c b/Doc/includes/custom4.c
index b0b2906..584992f 100644
--- a/Doc/includes/custom4.c
+++ b/Doc/includes/custom4.c
@@ -193,6 +193,11 @@
         return NULL;
 
     Py_INCREF(&CustomType);
-    PyModule_AddObject(m, "Custom", (PyObject *) &CustomType);
+    if (PyModule_AddObject(m, "Custom", (PyObject *) &CustomType) < 0) {
+        Py_DECREF(&CustomType);
+        Py_DECREF(m);
+        return NULL;
+    }
+
     return m;
 }
diff --git a/Doc/includes/sublist.c b/Doc/includes/sublist.c
index 76ff939..b2c26e7 100644
--- a/Doc/includes/sublist.c
+++ b/Doc/includes/sublist.c
@@ -59,6 +59,11 @@
         return NULL;
 
     Py_INCREF(&SubListType);
-    PyModule_AddObject(m, "SubList", (PyObject *) &SubListType);
+    if (PyModule_AddObject(m, "SubList", (PyObject *) &SubListType) < 0) {
+        Py_DECREF(&SubListType);
+        Py_DECREF(m);
+        return NULL;
+    }
+
     return m;
 }