diff --git a/Doc/c-api/bytearray.rst b/Doc/c-api/bytearray.rst
index 61b29ff..95ded96 100644
--- a/Doc/c-api/bytearray.rst
+++ b/Doc/c-api/bytearray.rst
@@ -16,7 +16,8 @@
 .. c:var:: PyTypeObject PyByteArray_Type
 
    This instance of :c:type:`PyTypeObject` represents the Python bytearray type;
-   it is the same object as ``bytearray`` in the Python layer.
+   it is the same object as :class:`bytearray` in the Python layer.
+
 
 Type check macros
 ^^^^^^^^^^^^^^^^^
diff --git a/Doc/c-api/bytes.rst b/Doc/c-api/bytes.rst
index b7d57fa..12ec80c 100644
--- a/Doc/c-api/bytes.rst
+++ b/Doc/c-api/bytes.rst
@@ -18,10 +18,8 @@
 
 .. c:var:: PyTypeObject PyBytes_Type
 
-   .. index:: single: BytesType (in module types)
-
    This instance of :c:type:`PyTypeObject` represents the Python bytes type; it
-   is the same object as ``bytes`` in the Python layer. .
+   is the same object as :class:`bytes` in the Python layer.
 
 
 .. c:function:: int PyBytes_Check(PyObject *o)
diff --git a/Doc/c-api/complex.rst b/Doc/c-api/complex.rst
index c66587a..43dfe56 100644
--- a/Doc/c-api/complex.rst
+++ b/Doc/c-api/complex.rst
@@ -82,7 +82,7 @@
 .. c:var:: PyTypeObject PyComplex_Type
 
    This instance of :c:type:`PyTypeObject` represents the Python complex number
-   type. It is the same object as ``complex`` and ``types.ComplexType``.
+   type. It is the same object as :class:`complex` in the Python layer.
 
 
 .. c:function:: int PyComplex_Check(PyObject *p)
diff --git a/Doc/c-api/dict.rst b/Doc/c-api/dict.rst
index 4ea71bc..836b108 100644
--- a/Doc/c-api/dict.rst
+++ b/Doc/c-api/dict.rst
@@ -15,13 +15,8 @@
 
 .. c:var:: PyTypeObject PyDict_Type
 
-   .. index::
-      single: DictType (in module types)
-      single: DictionaryType (in module types)
-
    This instance of :c:type:`PyTypeObject` represents the Python dictionary
-   type.  This is exposed to Python programs as ``dict`` and
-   ``types.DictType``.
+   type.  This is the same object as :class:`dict` in the Python layer.
 
 
 .. c:function:: int PyDict_Check(PyObject *p)
diff --git a/Doc/c-api/float.rst b/Doc/c-api/float.rst
index 5fb8a1c..757efd3 100644
--- a/Doc/c-api/float.rst
+++ b/Doc/c-api/float.rst
@@ -15,10 +15,8 @@
 
 .. c:var:: PyTypeObject PyFloat_Type
 
-   .. index:: single: FloatType (in modules types)
-
    This instance of :c:type:`PyTypeObject` represents the Python floating point
-   type.  This is the same object as ``float`` and ``types.FloatType``.
+   type.  This is the same object as :class:`float` in the Python layer.
 
 
 .. c:function:: int PyFloat_Check(PyObject *p)
diff --git a/Doc/c-api/list.rst b/Doc/c-api/list.rst
index f7d050a..25a13e9 100644
--- a/Doc/c-api/list.rst
+++ b/Doc/c-api/list.rst
@@ -15,8 +15,8 @@
 
 .. c:var:: PyTypeObject PyList_Type
 
-   This instance of :c:type:`PyTypeObject` represents the Python list type.  This
-   is the same object as ``list`` in the Python layer.
+   This instance of :c:type:`PyTypeObject` represents the Python list type.
+   This is the same object as :class:`list` in the Python layer.
 
 
 .. c:function:: int PyList_Check(PyObject *p)
diff --git a/Doc/c-api/long.rst b/Doc/c-api/long.rst
index 6ae1fb6..b2295e0 100644
--- a/Doc/c-api/long.rst
+++ b/Doc/c-api/long.rst
@@ -18,7 +18,7 @@
 .. c:var:: PyTypeObject PyLong_Type
 
    This instance of :c:type:`PyTypeObject` represents the Python integer type.
-   This is the same object as ``int``.
+   This is the same object as :class:`int` in the Python layer.
 
 
 .. c:function:: int PyLong_Check(PyObject *p)
diff --git a/Doc/c-api/slice.rst b/Doc/c-api/slice.rst
index 5f2a05a..5f992f1 100644
--- a/Doc/c-api/slice.rst
+++ b/Doc/c-api/slice.rst
@@ -8,10 +8,8 @@
 
 .. c:var:: PyTypeObject PySlice_Type
 
-   .. index:: single: SliceType (in module types)
-
-   The type object for slice objects.  This is the same as ``slice`` and
-   ``types.SliceType``.
+   The type object for slice objects.  This is the same as :class:`slice` in the
+   Python layer.
 
 
 .. c:function:: int PySlice_Check(PyObject *ob)
diff --git a/Doc/c-api/tuple.rst b/Doc/c-api/tuple.rst
index 7f6a79c..3cbfe5b 100644
--- a/Doc/c-api/tuple.rst
+++ b/Doc/c-api/tuple.rst
@@ -15,10 +15,8 @@
 
 .. c:var:: PyTypeObject PyTuple_Type
 
-   .. index:: single: TupleType (in module types)
-
-   This instance of :c:type:`PyTypeObject` represents the Python tuple type; it is
-   the same object as ``tuple`` and ``types.TupleType`` in the Python layer..
+   This instance of :c:type:`PyTypeObject` represents the Python tuple type; it
+   is the same object as :class:`tuple` in the Python layer.
 
 
 .. c:function:: int PyTuple_Check(PyObject *p)
diff --git a/Doc/c-api/type.rst b/Doc/c-api/type.rst
index 431d79e..49dfb3f 100644
--- a/Doc/c-api/type.rst
+++ b/Doc/c-api/type.rst
@@ -15,10 +15,8 @@
 
 .. c:var:: PyObject* PyType_Type
 
-   .. index:: single: TypeType (in module types)
-
-   This is the type object for type objects; it is the same object as ``type`` and
-   ``types.TypeType`` in the Python layer.
+   This is the type object for type objects; it is the same object as
+   :class:`type` in the Python layer.
 
 
 .. c:function:: int PyType_Check(PyObject *o)