diff --git a/Doc/c-api/bytearray.rst b/Doc/c-api/bytearray.rst
index 4bf3cfe100c..456f7d89bca 100644
--- a/Doc/c-api/bytearray.rst
+++ b/Doc/c-api/bytearray.rst
@@ -5,7 +5,7 @@
 Byte Array Objects
 ------------------
 
-.. index:: object: bytearray
+.. index:: pair: object; bytearray
 
 
 .. c:type:: PyByteArrayObject
diff --git a/Doc/c-api/bytes.rst b/Doc/c-api/bytes.rst
index d62962cab45..9f48f2ffafe 100644
--- a/Doc/c-api/bytes.rst
+++ b/Doc/c-api/bytes.rst
@@ -8,7 +8,7 @@ Bytes Objects
 These functions raise :exc:`TypeError` when expecting a bytes parameter and
 called with a non-bytes parameter.
 
-.. index:: object: bytes
+.. index:: pair: object; bytes
 
 
 .. c:type:: PyBytesObject
diff --git a/Doc/c-api/capsule.rst b/Doc/c-api/capsule.rst
index 1c8f432505e..427ed959c58 100644
--- a/Doc/c-api/capsule.rst
+++ b/Doc/c-api/capsule.rst
@@ -5,7 +5,7 @@
 Capsules
 --------
 
-.. index:: object: Capsule
+.. index:: pair: object; Capsule
 
 Refer to :ref:`using-capsules` for more information on using these objects.
 
diff --git a/Doc/c-api/complex.rst b/Doc/c-api/complex.rst
index 9228ce85200..344da903da4 100644
--- a/Doc/c-api/complex.rst
+++ b/Doc/c-api/complex.rst
@@ -5,7 +5,7 @@
 Complex Number Objects
 ----------------------
 
-.. index:: object: complex number
+.. index:: pair: object; complex number
 
 Python's complex number objects are implemented as two distinct types when
 viewed from the C API:  one is the Python object exposed to Python programs, and
diff --git a/Doc/c-api/concrete.rst b/Doc/c-api/concrete.rst
index 8d3124a12fa..880f7b15ce6 100644
--- a/Doc/c-api/concrete.rst
+++ b/Doc/c-api/concrete.rst
@@ -40,7 +40,7 @@ This section describes Python type objects and the singleton object ``None``.
 Numeric Objects
 ===============
 
-.. index:: object: numeric
+.. index:: pair: object; numeric
 
 .. toctree::
 
@@ -55,7 +55,7 @@ Numeric Objects
 Sequence Objects
 ================
 
-.. index:: object: sequence
+.. index:: pair: object; sequence
 
 Generic operations on sequence objects were discussed in the previous chapter;
 this section deals with the specific kinds of sequence objects that are
@@ -77,7 +77,7 @@ intrinsic to the Python language.
 Container Objects
 =================
 
-.. index:: object: mapping
+.. index:: pair: object; mapping
 
 .. toctree::
 
diff --git a/Doc/c-api/dict.rst b/Doc/c-api/dict.rst
index b9f84cea785..f02abb01f02 100644
--- a/Doc/c-api/dict.rst
+++ b/Doc/c-api/dict.rst
@@ -5,7 +5,7 @@
 Dictionary Objects
 ------------------
 
-.. index:: object: dictionary
+.. index:: pair: object; dictionary
 
 
 .. c:type:: PyDictObject
diff --git a/Doc/c-api/file.rst b/Doc/c-api/file.rst
index 58ed58e5466..f32ecba9f27 100644
--- a/Doc/c-api/file.rst
+++ b/Doc/c-api/file.rst
@@ -5,7 +5,7 @@
 File Objects
 ------------
 
-.. index:: object: file
+.. index:: pair: object; file
 
 These APIs are a minimal emulation of the Python 2 C API for built-in file
 objects, which used to rely on the buffered I/O (:c:expr:`FILE*`) support
diff --git a/Doc/c-api/float.rst b/Doc/c-api/float.rst
index 023b12c20b7..05b2d100d57 100644
--- a/Doc/c-api/float.rst
+++ b/Doc/c-api/float.rst
@@ -5,7 +5,7 @@
 Floating Point Objects
 ----------------------
 
-.. index:: object: floating point
+.. index:: pair: object; floating point
 
 
 .. c:type:: PyFloatObject
diff --git a/Doc/c-api/function.rst b/Doc/c-api/function.rst
index 947ed704040..5857dba82c1 100644
--- a/Doc/c-api/function.rst
+++ b/Doc/c-api/function.rst
@@ -5,7 +5,7 @@
 Function Objects
 ----------------
 
-.. index:: object: function
+.. index:: pair: object; function
 
 There are a few functions specific to Python functions.
 
diff --git a/Doc/c-api/intro.rst b/Doc/c-api/intro.rst
index 1a200b919f0..8de76e55cd0 100644
--- a/Doc/c-api/intro.rst
+++ b/Doc/c-api/intro.rst
@@ -261,7 +261,7 @@ complete listing.
 Objects, Types and Reference Counts
 ===================================
 
-.. index:: object: type
+.. index:: pair: object; type
 
 Most Python/C API functions have one or more arguments as well as a return value
 of type :c:expr:`PyObject*`.  This type is a pointer to an opaque data type
diff --git a/Doc/c-api/list.rst b/Doc/c-api/list.rst
index f9e65354a25..317421f0db8 100644
--- a/Doc/c-api/list.rst
+++ b/Doc/c-api/list.rst
@@ -5,7 +5,7 @@
 List Objects
 ------------
 
-.. index:: object: list
+.. index:: pair: object; list
 
 
 .. c:type:: PyListObject
diff --git a/Doc/c-api/long.rst b/Doc/c-api/long.rst
index 41b5632d230..4a71c89ad85 100644
--- a/Doc/c-api/long.rst
+++ b/Doc/c-api/long.rst
@@ -5,8 +5,8 @@
 Integer Objects
 ---------------
 
-.. index:: object: long integer
-           object: integer
+.. index:: pair: object; long integer
+           pair: object; integer
 
 All integers are implemented as "long" integer objects of arbitrary size.
 
diff --git a/Doc/c-api/memoryview.rst b/Doc/c-api/memoryview.rst
index ebd5c776043..2aa43318e7a 100644
--- a/Doc/c-api/memoryview.rst
+++ b/Doc/c-api/memoryview.rst
@@ -3,7 +3,7 @@
 .. _memoryview-objects:
 
 .. index::
-   object: memoryview
+   pair: object; memoryview
 
 MemoryView objects
 ------------------
diff --git a/Doc/c-api/method.rst b/Doc/c-api/method.rst
index 6e7e1e21aa9..93ad30cd4f7 100644
--- a/Doc/c-api/method.rst
+++ b/Doc/c-api/method.rst
@@ -5,7 +5,7 @@
 Instance Method Objects
 -----------------------
 
-.. index:: object: instancemethod
+.. index:: pair: object; instancemethod
 
 An instance method is a wrapper for a :c:data:`PyCFunction` and the new way
 to bind a :c:data:`PyCFunction` to a class object. It replaces the former call
@@ -47,7 +47,7 @@ to bind a :c:data:`PyCFunction` to a class object. It replaces the former call
 Method Objects
 --------------
 
-.. index:: object: method
+.. index:: pair: object; method
 
 Methods are bound function objects. Methods are always bound to an instance of
 a user-defined class. Unbound methods (methods bound to a class object) are
diff --git a/Doc/c-api/module.rst b/Doc/c-api/module.rst
index c0351c8a6c7..230b471d473 100644
--- a/Doc/c-api/module.rst
+++ b/Doc/c-api/module.rst
@@ -5,7 +5,7 @@
 Module Objects
 --------------
 
-.. index:: object: module
+.. index:: pair: object; module
 
 
 .. c:var:: PyTypeObject PyModule_Type
diff --git a/Doc/c-api/none.rst b/Doc/c-api/none.rst
index 26d2b7aab20..b84a16a28ea 100644
--- a/Doc/c-api/none.rst
+++ b/Doc/c-api/none.rst
@@ -5,7 +5,7 @@
 The ``None`` Object
 -------------------
 
-.. index:: object: None
+.. index:: pair: object; None
 
 Note that the :c:type:`PyTypeObject` for ``None`` is not directly exposed in the
 Python/C API.  Since ``None`` is a singleton, testing for object identity (using
diff --git a/Doc/c-api/set.rst b/Doc/c-api/set.rst
index f0d905bae8a..8e8af602522 100644
--- a/Doc/c-api/set.rst
+++ b/Doc/c-api/set.rst
@@ -9,8 +9,8 @@ Set Objects
 
 
 .. index::
-   object: set
-   object: frozenset
+   pair: object; set
+   pair: object; frozenset
 
 This section details the public API for :class:`set` and :class:`frozenset`
 objects.  Any functionality not listed below is best accessed using either
diff --git a/Doc/c-api/tuple.rst b/Doc/c-api/tuple.rst
index 5acddf7849a..ac62058676e 100644
--- a/Doc/c-api/tuple.rst
+++ b/Doc/c-api/tuple.rst
@@ -5,7 +5,7 @@
 Tuple Objects
 -------------
 
-.. index:: object: tuple
+.. index:: pair: object; tuple
 
 
 .. c:type:: PyTupleObject
diff --git a/Doc/c-api/type.rst b/Doc/c-api/type.rst
index c21fd9255d2..fb38935e003 100644
--- a/Doc/c-api/type.rst
+++ b/Doc/c-api/type.rst
@@ -5,7 +5,7 @@
 Type Objects
 ------------
 
-.. index:: object: type
+.. index:: pair: object; type
 
 
 .. c:type:: PyTypeObject
diff --git a/Doc/library/functions.rst b/Doc/library/functions.rst
index ddb918de115..5a022edb75b 100644
--- a/Doc/library/functions.rst
+++ b/Doc/library/functions.rst
@@ -1830,7 +1830,7 @@ are always available.  They are listed here in alphabetical order.
 .. class:: type(object)
            type(name, bases, dict, **kwds)
 
-   .. index:: object: type
+   .. index:: pair: object; type
 
    With one argument, return the type of an *object*.  The return value is a
    type object and generally the same object as returned by
diff --git a/Doc/library/socket.rst b/Doc/library/socket.rst
index 150c1f93afd..4ee0897db94 100644
--- a/Doc/library/socket.rst
+++ b/Doc/library/socket.rst
@@ -19,7 +19,7 @@ all modern Unix systems, Windows, MacOS, and probably additional platforms.
 
 .. include:: ../includes/wasm-notavail.rst
 
-.. index:: object: socket
+.. index:: pair: object; socket
 
 The Python interface is a straightforward transliteration of the Unix system
 call and library interface for sockets to Python's object-oriented style: the
diff --git a/Doc/library/stdtypes.rst b/Doc/library/stdtypes.rst
index 46b0389adaa..2f549f2e97c 100644
--- a/Doc/library/stdtypes.rst
+++ b/Doc/library/stdtypes.rst
@@ -205,11 +205,11 @@ Numeric Types --- :class:`int`, :class:`float`, :class:`complex`
 ================================================================
 
 .. index::
-   object: numeric
-   object: Boolean
-   object: integer
-   object: floating point
-   object: complex number
+   pair: object; numeric
+   pair: object; Boolean
+   pair: object; integer
+   pair: object; floating point
+   pair: object; complex number
    pair: C; language
 
 There are three distinct numeric types: :dfn:`integers`, :dfn:`floating
@@ -927,7 +927,7 @@ described in dedicated sections.
 Common Sequence Operations
 --------------------------
 
-.. index:: object: sequence
+.. index:: pair: object; sequence
 
 The operations in the following table are supported by most sequence types,
 both mutable and immutable. The :class:`collections.abc.Sequence` ABC is
@@ -1112,7 +1112,7 @@ Immutable Sequence Types
 
 .. index::
    triple: immutable; sequence; types
-   object: tuple
+   pair: object; tuple
    builtin: hash
 
 The only operation that immutable sequence types generally implement that is
@@ -1134,8 +1134,8 @@ Mutable Sequence Types
 
 .. index::
    triple: mutable; sequence; types
-   object: list
-   object: bytearray
+   pair: object; list
+   pair: object; bytearray
 
 The operations in the following table are defined on mutable sequence types.
 The :class:`collections.abc.MutableSequence` ABC is provided to make it
@@ -1252,7 +1252,7 @@ Notes:
 Lists
 -----
 
-.. index:: object: list
+.. index:: pair: object; list
 
 Lists are mutable sequences, typically used to store collections of
 homogeneous items (where the precise degree of similarity will vary by
@@ -1331,7 +1331,7 @@ application).
 Tuples
 ------
 
-.. index:: object: tuple
+.. index:: pair: object; tuple
 
 Tuples are immutable sequences, typically used to store collections of
 heterogeneous data (such as the 2-tuples produced by the :func:`enumerate`
@@ -1375,7 +1375,7 @@ choice than a simple tuple object.
 Ranges
 ------
 
-.. index:: object: range
+.. index:: pair: object; range
 
 The :class:`range` type represents an immutable sequence of numbers and is
 commonly used for looping a specific number of times in :keyword:`for`
@@ -1500,7 +1500,7 @@ objects that compare equal might have different :attr:`~range.start`,
 .. index::
    single: string; text sequence type
    single: str (built-in class); (see also string)
-   object: string
+   pair: object; string
 
 .. _textseq:
 
@@ -1534,7 +1534,7 @@ Since there is no separate "character" type, indexing a string produces
 strings of length 1. That is, for a non-empty string *s*, ``s[0] == s[0:1]``.
 
 .. index::
-   object: io.StringIO
+   pair: object; io.StringIO
 
 There is also no mutable string type, but :meth:`str.join` or
 :class:`io.StringIO` can be used to efficiently construct strings from
@@ -2508,9 +2508,9 @@ Binary Sequence Types --- :class:`bytes`, :class:`bytearray`, :class:`memoryview
 =================================================================================
 
 .. index::
-   object: bytes
-   object: bytearray
-   object: memoryview
+   pair: object; bytes
+   pair: object; bytearray
+   pair: object; memoryview
    pair: module; array
 
 The core built-in types for manipulating binary data are :class:`bytes` and
@@ -2526,7 +2526,7 @@ The :mod:`array` module supports efficient storage of basic data types like
 Bytes Objects
 -------------
 
-.. index:: object: bytes
+.. index:: pair: object; bytes
 
 Bytes objects are immutable sequences of single bytes. Since many major
 binary protocols are based on the ASCII text encoding, bytes objects offer
@@ -2633,7 +2633,7 @@ always convert a bytes object into a list of integers using ``list(b)``.
 Bytearray Objects
 -----------------
 
-.. index:: object: bytearray
+.. index:: pair: object; bytearray
 
 :class:`bytearray` objects are a mutable counterpart to :class:`bytes`
 objects.
@@ -4212,7 +4212,7 @@ copying.
 Set Types --- :class:`set`, :class:`frozenset`
 ==============================================
 
-.. index:: object: set
+.. index:: pair: object; set
 
 A :dfn:`set` object is an unordered collection of distinct :term:`hashable` objects.
 Common uses include membership testing, removing duplicates from a sequence, and
@@ -4414,8 +4414,8 @@ Mapping Types --- :class:`dict`
 ===============================
 
 .. index::
-   object: mapping
-   object: dictionary
+   pair: object; mapping
+   pair: object; dictionary
    triple: operations on; mapping; types
    triple: operations on; dictionary; type
    statement: del
@@ -4889,7 +4889,7 @@ Generic Alias Type
 ------------------
 
 .. index::
-   object: GenericAlias
+   pair: object; GenericAlias
    pair: Generic; Alias
 
 ``GenericAlias`` objects are generally created by
@@ -5144,7 +5144,7 @@ Union Type
 ----------
 
 .. index::
-   object: Union
+   pair: object; Union
    pair: union; type
 
 A union object holds the value of the ``|`` (bitwise or) operation on
@@ -5301,7 +5301,7 @@ See :ref:`function` for more information.
 Methods
 -------
 
-.. index:: object: method
+.. index:: pair: object; method
 
 Methods are functions that are called using the attribute notation. There are
 two flavors: built-in methods (such as :meth:`append` on lists) and class
diff --git a/Doc/library/sys.rst b/Doc/library/sys.rst
index 57a0d0a1258..bacf8ceac50 100644
--- a/Doc/library/sys.rst
+++ b/Doc/library/sys.rst
@@ -444,7 +444,7 @@ always available.
    object <traceback-objects>` which typically encapsulates the call
    stack at the point where the exception last occurred.
 
-   .. index:: object: traceback
+   .. index:: pair: object; traceback
 
    If no exception is being handled anywhere on the stack, this function
    return a tuple containing three ``None`` values.
diff --git a/Doc/library/traceback.rst b/Doc/library/traceback.rst
index 561c8529046..5c0e261b907 100644
--- a/Doc/library/traceback.rst
+++ b/Doc/library/traceback.rst
@@ -14,7 +14,7 @@ interpreter when it prints a stack trace.  This is useful when you want to print
 stack traces under program control, such as in a "wrapper" around the
 interpreter.
 
-.. index:: object: traceback
+.. index:: pair: object; traceback
 
 The module uses traceback objects --- these are objects of type :class:`types.TracebackType`,
 which are assigned to the ``__traceback__`` field of :class:`BaseException` instances.
diff --git a/Doc/reference/compound_stmts.rst b/Doc/reference/compound_stmts.rst
index 1f03180f156..5750d3149c8 100644
--- a/Doc/reference/compound_stmts.rst
+++ b/Doc/reference/compound_stmts.rst
@@ -147,7 +147,7 @@ The :keyword:`!for` statement
    pair: keyword; else
    pair: target; list
    pair: loop; statement
-   object: sequence
+   pair: object; sequence
    single: : (colon); compound statement
 
 The :keyword:`for` statement is used to iterate over the elements of a sequence
@@ -298,7 +298,7 @@ keeping all locals in that frame alive until the next garbage collection occurs.
 
 .. index::
    pair: module; sys
-   object: traceback
+   pair: object; traceback
 
 Before an :keyword:`!except` clause's suite is executed,
 the exception is stored in the :mod:`sys` module, where it can be accessed
@@ -1194,8 +1194,8 @@ Function definitions
    pair: function; definition
    pair: function; name
    pair: name; binding
-   object: user-defined function
-   object: function
+   pair: object; user-defined function
+   pair: object; function
    pair: function; name
    pair: name; binding
    single: () (parentheses); function definition
@@ -1363,7 +1363,7 @@ Class definitions
 =================
 
 .. index::
-   object: class
+   pair: object; class
    statement: class
    pair: class; definition
    pair: class; name
diff --git a/Doc/reference/datamodel.rst b/Doc/reference/datamodel.rst
index 9d3ea3f78de..18906a005b2 100644
--- a/Doc/reference/datamodel.rst
+++ b/Doc/reference/datamodel.rst
@@ -142,7 +142,7 @@ attributes.'  These are attributes that provide access to the implementation and
 are not intended for general use.  Their definition may change in the future.
 
 None
-   .. index:: object: None
+   .. index:: pair: object; None
 
    This type has a single value.  There is a single object with this value. This
    object is accessed through the built-in name ``None``. It is used to signify the
@@ -150,7 +150,7 @@ None
    don't explicitly return anything. Its truth value is false.
 
 NotImplemented
-   .. index:: object: NotImplemented
+   .. index:: pair: object; NotImplemented
 
    This type has a single value.  There is a single object with this value. This
    object is accessed through the built-in name ``NotImplemented``. Numeric methods
@@ -171,7 +171,7 @@ NotImplemented
 
 Ellipsis
    .. index::
-      object: Ellipsis
+      pair: object; Ellipsis
       single: ...; ellipsis literal
 
    This type has a single value.  There is a single object with this value. This
@@ -179,7 +179,7 @@ Ellipsis
    ``Ellipsis``.  Its truth value is true.
 
 :class:`numbers.Number`
-   .. index:: object: numeric
+   .. index:: pair: object; numeric
 
    These are created by numeric literals and returned as results by arithmetic
    operators and arithmetic built-in functions.  Numeric objects are immutable;
@@ -209,7 +209,7 @@ Ellipsis
    numbers:
 
    :class:`numbers.Integral`
-      .. index:: object: integer
+      .. index:: pair: object; integer
 
       These represent elements from the mathematical set of integers (positive and
       negative).
@@ -225,7 +225,7 @@ Ellipsis
 
       Booleans (:class:`bool`)
          .. index::
-            object: Boolean
+            pair: object; Boolean
             single: False
             single: True
 
@@ -242,7 +242,7 @@ Ellipsis
 
    :class:`numbers.Real` (:class:`float`)
       .. index::
-         object: floating point
+         pair: object; floating point
          pair: floating point; number
          pair: C; language
          pair: Java; language
@@ -257,7 +257,7 @@ Ellipsis
 
    :class:`numbers.Complex` (:class:`complex`)
       .. index::
-         object: complex
+         pair: object; complex
          pair: complex; number
 
       These represent complex numbers as a pair of machine-level double precision
@@ -268,7 +268,7 @@ Ellipsis
 Sequences
    .. index::
       builtin: len
-      object: sequence
+      pair: object; sequence
       single: index operation
       single: item selection
       single: subscription
@@ -293,8 +293,8 @@ Sequences
 
    Immutable sequences
       .. index::
-         object: immutable sequence
-         object: immutable
+         pair: object; immutable sequence
+         pair: object; immutable
 
       An object of an immutable sequence type cannot change once it is created.  (If
       the object contains references to other objects, these other objects may be
@@ -328,7 +328,7 @@ Sequences
 
       Tuples
          .. index::
-            object: tuple
+            pair: object; tuple
             pair: singleton; tuple
             pair: empty; tuple
 
@@ -350,8 +350,8 @@ Sequences
 
    Mutable sequences
       .. index::
-         object: mutable sequence
-         object: mutable
+         pair: object; mutable sequence
+         pair: object; mutable
          pair: assignment; statement
          single: subscription
          single: slicing
@@ -363,7 +363,7 @@ Sequences
       There are currently two intrinsic mutable sequence types:
 
       Lists
-         .. index:: object: list
+         .. index:: pair: object; list
 
          The items of a list are arbitrary Python objects.  Lists are formed by
          placing a comma-separated list of expressions in square brackets. (Note
@@ -385,7 +385,7 @@ Sequences
 Set types
    .. index::
       builtin: len
-      object: set type
+      pair: object; set type
 
    These represent unordered, finite sets of unique, immutable objects. As such,
    they cannot be indexed by any subscript. However, they can be iterated over, and
@@ -402,14 +402,14 @@ Set types
    There are currently two intrinsic set types:
 
    Sets
-      .. index:: object: set
+      .. index:: pair: object; set
 
       These represent a mutable set. They are created by the built-in :func:`set`
       constructor and can be modified afterwards by several methods, such as
       :meth:`~set.add`.
 
    Frozen sets
-      .. index:: object: frozenset
+      .. index:: pair: object; frozenset
 
       These represent an immutable set.  They are created by the built-in
       :func:`frozenset` constructor.  As a frozenset is immutable and
@@ -420,7 +420,7 @@ Mappings
    .. index::
       builtin: len
       single: subscription
-      object: mapping
+      pair: object; mapping
 
    These represent finite sets of objects indexed by arbitrary index sets. The
    subscript notation ``a[k]`` selects the item indexed by ``k`` from the mapping
@@ -431,7 +431,7 @@ Mappings
    There is currently a single intrinsic mapping type:
 
    Dictionaries
-      .. index:: object: dictionary
+      .. index:: pair: object; dictionary
 
       These represent finite sets of objects indexed by nearly arbitrary values.  The
       only types of values not acceptable as keys are values containing lists or
@@ -465,7 +465,7 @@ Mappings
 
 Callable types
    .. index::
-      object: callable
+      pair: object; callable
       pair: function; call
       single: invocation
       pair: function; argument
@@ -476,8 +476,8 @@ Callable types
    User-defined functions
       .. index::
          pair: user-defined; function
-         object: function
-         object: user-defined function
+         pair: object; function
+         pair: object; user-defined function
 
       A user-defined function object is created by a function definition (see
       section :ref:`function`).  It should be called with an argument list
@@ -580,8 +580,8 @@ Callable types
 
    Instance methods
       .. index::
-         object: method
-         object: user-defined method
+         pair: object; method
+         pair: object; user-defined method
          pair: user-defined; method
 
       An instance method object combines a class, a class instance and any
@@ -688,8 +688,8 @@ Callable types
 
    Built-in functions
       .. index::
-         object: built-in function
-         object: function
+         pair: object; built-in function
+         pair: object; function
          pair: C; language
 
       A built-in function object is a wrapper around a C function.  Examples of
@@ -703,8 +703,8 @@ Callable types
 
    Built-in methods
       .. index::
-         object: built-in method
-         object: method
+         pair: object; built-in method
+         pair: object; method
          pair: built-in; method
 
       This is really a different disguise of a built-in function, this time containing
@@ -728,7 +728,7 @@ Callable types
 Modules
    .. index::
       statement: import
-      object: module
+      pair: object; module
 
    Modules are a basic organizational unit of Python code, and are created by
    the :ref:`import system <importsystem>` as invoked either by the
@@ -805,12 +805,12 @@ Custom classes
    .. XXX: Could we add that MRO doc as an appendix to the language ref?
 
    .. index::
-      object: class
-      object: class instance
-      object: instance
+      pair: object; class
+      pair: object; class instance
+      pair: object; instance
       pair: class object; call
       single: container
-      object: dictionary
+      pair: object; dictionary
       pair: class; attribute
 
    When a class attribute reference (for class :class:`C`, say) would yield a
@@ -865,8 +865,8 @@ Custom classes
 
 Class instances
    .. index::
-      object: class instance
-      object: instance
+      pair: object; class instance
+      pair: object; instance
       pair: class; instance
       pair: class instance; attribute
 
@@ -892,9 +892,9 @@ Class instances
    dictionary directly.
 
    .. index::
-      object: numeric
-      object: sequence
-      object: mapping
+      pair: object; numeric
+      pair: object; sequence
+      pair: object; mapping
 
    Class instances can pretend to be numbers, sequences, or mappings if they have
    methods with certain special names.  See section :ref:`specialnames`.
@@ -996,7 +996,7 @@ Internal types
       required stack size; :attr:`co_flags` is an integer encoding a number
       of flags for the interpreter.
 
-      .. index:: object: generator
+      .. index:: pair: object; generator
 
       The following flag bits are defined for :attr:`co_flags`: bit ``0x04`` is set if
       the function uses the ``*arguments`` syntax to accept an arbitrary number of
@@ -1053,7 +1053,7 @@ Internal types
    .. _frame-objects:
 
    Frame objects
-      .. index:: object: frame
+      .. index:: pair: object; frame
 
       Frame objects represent execution frames.  They may occur in traceback objects
       (see below), and are also passed to registered trace functions.
@@ -1116,7 +1116,7 @@ Internal types
 
    Traceback objects
       .. index::
-         object: traceback
+         pair: object; traceback
          pair: stack; trace
          pair: exception; handler
          pair: execution; stack
@@ -1498,7 +1498,7 @@ Basic customization
 .. method:: object.__hash__(self)
 
    .. index::
-      object: dictionary
+      pair: object; dictionary
       builtin: hash
 
    Called by built-in function :func:`hash` and for operations on members of
@@ -2506,7 +2506,7 @@ through the object's keys; for sequences, it should iterate through the values.
    .. versionadded:: 3.4
 
 
-.. index:: object: slice
+.. index:: pair: object; slice
 
 .. note::
 
diff --git a/Doc/reference/expressions.rst b/Doc/reference/expressions.rst
index b1bb162f62e..78185657bf8 100644
--- a/Doc/reference/expressions.rst
+++ b/Doc/reference/expressions.rst
@@ -245,7 +245,7 @@ List displays
    pair: list; display
    pair: list; comprehensions
    pair: empty; list
-   object: list
+   pair: object; list
    single: [] (square brackets); list expression
    single: , (comma); expression list
 
@@ -270,7 +270,7 @@ Set displays
 .. index::
    pair: set; display
    pair: set; comprehensions
-   object: set
+   pair: object; set
    single: {} (curly brackets); set expression
    single: , (comma); expression list
 
@@ -299,7 +299,7 @@ Dictionary displays
    pair: dictionary; display
    pair: dictionary; comprehensions
    key, datum, key/datum pair
-   object: dictionary
+   pair: object; dictionary
    single: {} (curly brackets); dictionary expression
    single: : (colon); in dictionary expressions
    single: , (comma); in dictionary displays
@@ -361,7 +361,7 @@ Generator expressions
 
 .. index::
    pair: generator; expression
-   object: generator
+   pair: object; generator
    single: () (parentheses); generator expression
 
 A generator expression is a compact generator notation in parentheses:
@@ -522,7 +522,7 @@ on the right hand side of an assignment statement.
       The proposal that expanded on :pep:`492` by adding generator capabilities to
       coroutine functions.
 
-.. index:: object: generator
+.. index:: pair: object; generator
 .. _generator-methods:
 
 Generator-iterator methods
@@ -701,7 +701,7 @@ of a *finalizer* method see the implementation of
 The expression ``yield from <expr>`` is a syntax error when used in an
 asynchronous generator function.
 
-.. index:: object: asynchronous-generator
+.. index:: pair: object; asynchronous-generator
 .. _asynchronous-generator-methods:
 
 Asynchronous generator-iterator methods
@@ -811,8 +811,8 @@ An attribute reference is a primary followed by a period and a name:
 
 .. index::
    exception: AttributeError
-   object: module
-   object: list
+   pair: object; module
+   pair: object; list
 
 The primary must evaluate to an object of a type that supports attribute
 references, which most objects do.  This object is then asked to produce the
@@ -833,12 +833,12 @@ Subscriptions
    single: [] (square brackets); subscription
 
 .. index::
-   object: sequence
-   object: mapping
-   object: string
-   object: tuple
-   object: list
-   object: dictionary
+   pair: object; sequence
+   pair: object; mapping
+   pair: object; string
+   pair: object; tuple
+   pair: object; list
+   pair: object; dictionary
    pair: sequence; item
 
 The subscription of an instance of a :ref:`container class <sequence-types>`
@@ -906,10 +906,10 @@ Slicings
    single: , (comma); slicing
 
 .. index::
-   object: sequence
-   object: string
-   object: tuple
-   object: list
+   pair: object; sequence
+   pair: object; string
+   pair: object; tuple
+   pair: object; list
 
 A slicing selects a range of items in a sequence object (e.g., a string, tuple
 or list).  Slicings may be used as expressions or as targets in assignment or
@@ -950,7 +950,7 @@ substituting ``None`` for missing expressions.
 
 
 .. index::
-   object: callable
+   pair: object; callable
    single: call
    single: argument; call semantics
    single: () (parentheses); call
@@ -1100,8 +1100,8 @@ a user-defined function:
    .. index::
       pair: function; call
       triple: user-defined; function; call
-      object: user-defined function
-      object: function
+      pair: object; user-defined function
+      pair: object; function
 
    The code block for the function is executed, passing it the argument list.  The
    first thing the code block will do is bind the formal parameters to the
@@ -1115,25 +1115,25 @@ a built-in function or method:
       pair: built-in function; call
       pair: method; call
       pair: built-in method; call
-      object: built-in method
-      object: built-in function
-      object: method
-      object: function
+      pair: object; built-in method
+      pair: object; built-in function
+      pair: object; method
+      pair: object; function
 
    The result is up to the interpreter; see :ref:`built-in-funcs` for the
    descriptions of built-in functions and methods.
 
 a class object:
    .. index::
-      object: class
+      pair: object; class
       pair: class object; call
 
    A new instance of that class is returned.
 
 a class instance method:
    .. index::
-      object: class instance
-      object: instance
+      pair: object; class instance
+      pair: object; instance
       pair: class instance; call
 
    The corresponding user-defined function is called, with an argument list that is
@@ -1672,7 +1672,7 @@ if :keyword:`in` raised that exception).
    pair: operator; in
    pair: operator; not in
    pair: membership; test
-   object: sequence
+   pair: object; sequence
 
 The operator :keyword:`not in` is defined to have the inverse truth value of
 :keyword:`in`.
@@ -1854,7 +1854,7 @@ Expression lists
    starred_expression: `expression` | (`starred_item` ",")* [`starred_item`]
    starred_item: `assignment_expression` | "*" `or_expr`
 
-.. index:: object: tuple
+.. index:: pair: object; tuple
 
 Except when part of a list or set display, an expression list
 containing at least one comma yields a tuple.  The length of
diff --git a/Doc/reference/simple_stmts.rst b/Doc/reference/simple_stmts.rst
index 5c7b5d7efaa..acc3998e09b 100644
--- a/Doc/reference/simple_stmts.rst
+++ b/Doc/reference/simple_stmts.rst
@@ -54,7 +54,7 @@ expression).
 
 .. index::
    builtin: repr
-   object: None
+   pair: object; None
    pair: string; conversion
    single: output
    pair: standard; output
@@ -76,7 +76,7 @@ Assignment statements
    pair: assignment; statement
    pair: binding; name
    pair: rebinding; name
-   object: mutable
+   pair: object; mutable
    pair: attribute; assignment
 
 Assignment statements are used to (re)bind names to values and to modify
@@ -185,7 +185,7 @@ Assignment of an object to a single target is recursively defined as follows.
 
   .. index::
      pair: subscription; assignment
-     object: mutable
+     pair: object; mutable
 
 * If the target is a subscription: The primary expression in the reference is
   evaluated.  It should yield either a mutable sequence object (such as a list)
@@ -193,8 +193,8 @@ Assignment of an object to a single target is recursively defined as follows.
   evaluated.
 
   .. index::
-     object: sequence
-     object: list
+     pair: object; sequence
+     pair: object; list
 
   If the primary is a mutable sequence object (such as a list), the subscript
   must yield an integer.  If it is negative, the sequence's length is added to
@@ -204,8 +204,8 @@ Assignment of an object to a single target is recursively defined as follows.
   raised (assignment to a subscripted sequence cannot add new items to a list).
 
   .. index::
-     object: mapping
-     object: dictionary
+     pair: object; mapping
+     pair: object; dictionary
 
   If the primary is a mapping object (such as a dictionary), the subscript must
   have a type compatible with the mapping's key type, and the mapping is then
@@ -574,7 +574,7 @@ instantiating the class with no arguments.
 The :dfn:`type` of the exception is the exception instance's class, the
 :dfn:`value` is the instance itself.
 
-.. index:: object: traceback
+.. index:: pair: object; traceback
 
 A traceback object is normally created automatically when an exception is raised
 and attached to it as the :attr:`__traceback__` attribute, which is writable.
diff --git a/Doc/tools/extensions/pyspecific.py b/Doc/tools/extensions/pyspecific.py
index 8ca3ef04523..41016113d25 100644
--- a/Doc/tools/extensions/pyspecific.py
+++ b/Doc/tools/extensions/pyspecific.py
@@ -692,7 +692,7 @@ def patch_pairindextypes(app) -> None:
         pairindextypes.pop('module', None)
         pairindextypes.pop('keyword', None)
         pairindextypes.pop('operator', None)
-        # pairindextypes.pop('object', None)
+        pairindextypes.pop('object', None)
         # pairindextypes.pop('exception', None)
         # pairindextypes.pop('statement', None)
         # pairindextypes.pop('builtin', None)
diff --git a/Doc/tutorial/classes.rst b/Doc/tutorial/classes.rst
index 116801177a3..06445e000c1 100644
--- a/Doc/tutorial/classes.rst
+++ b/Doc/tutorial/classes.rst
@@ -344,7 +344,7 @@ list objects have methods called append, insert, remove, sort, and so on.
 However, in the following discussion, we'll use the term method exclusively to
 mean methods of class instance objects, unless explicitly stated otherwise.)
 
-.. index:: object: method
+.. index:: pair: object; method
 
 Valid method names of an instance object depend on its class.  By definition,
 all attributes of a class that are function  objects define corresponding
diff --git a/Doc/tutorial/inputoutput.rst b/Doc/tutorial/inputoutput.rst
index aeacc1559a2..3fcf4e3f43a 100644
--- a/Doc/tutorial/inputoutput.rst
+++ b/Doc/tutorial/inputoutput.rst
@@ -286,7 +286,7 @@ Reading and Writing Files
 
 .. index::
    builtin: open
-   object: file
+   pair: object; file
 
 :func:`open` returns a :term:`file object`, and is most commonly used with
 two positional arguments and one keyword argument: