Removed the API to create unbound methods and simplified the API for bound methods. The signature is PyMethod_New(func, instance).

Also removed im_class and renamed im_self to __self__ and im_func to __func__. im_class can be substituted with method.__self__.__class__.
I've also updated some parts of the documenation.

Doc/library/inspect.rst

@@ -49,14 +49,11 @@ attributes:
 |           | __name__        | name with which this      |
 |           |                 | method was defined        |
 +-----------+-----------------+---------------------------+
-|           | im_class        | class object that asked   |
-|           |                 | for this method           |
-+-----------+-----------------+---------------------------+
-|           | im_func         | function object           |
+|           | __func__        | function object           |
 |           |                 | containing implementation |
 |           |                 | of method                 |
 +-----------+-----------------+---------------------------+
-|           | im_self         | instance to which this    |
+|           | __self__        | instance to which this    |
 |           |                 | method is bound, or       |
 |           |                 | ``None``                  |
 +-----------+-----------------+---------------------------+
@@ -264,7 +261,7 @@ attributes:
    Methods implemented via descriptors that also pass one of the other tests
    return false from the :func:`ismethoddescriptor` test, simply because the
    other tests promise more -- you can, e.g., count on having the
-   :attr:`im_func` attribute (etc) when an object passes :func:`ismethod`.
+   :attr:`__func__` attribute (etc) when an object passes :func:`ismethod`.
 
 
 .. function:: isdatadescriptor(object)

Doc/library/new.rst

@@ -17,10 +17,10 @@ non-sensical arguments which crash the interpreter when the object is used.
 The :mod:`new` module defines the following functions:
 
 
-.. function:: instancemethod(function, instance, class)
+.. function:: instancemethod(function, instance)
 
-   This function will return a method object, bound to *instance*, or unbound if
-   *instance* is ``None``.  *function* must be callable.
+   This function will return a method object, bound to *instance*.
+   *function* must be callable.
 
 
 .. function:: function(code, globals[, name[, argdefs[, closure]]])

Doc/library/stdtypes.rst

@@ -2216,21 +2216,21 @@ instance methods.  Built-in methods are described with the types that support
 them.
 
 The implementation adds two special read-only attributes to class instance
-methods: ``m.im_self`` is the object on which the method operates, and
-``m.im_func`` is the function implementing the method.  Calling ``m(arg-1,
-arg-2, ..., arg-n)`` is completely equivalent to calling ``m.im_func(m.im_self,
-arg-1, arg-2, ..., arg-n)``.
+methods: ``m.__self__`` is the object on which the method operates, and
+``m.__func__`` is the function implementing the method.  Calling ``m(arg-1,
+arg-2, ..., arg-n)`` is completely equivalent to calling ``m.__func__(
+m.__self__, arg-1, arg-2, ..., arg-n)``.
 
 Class instance methods are either *bound* or *unbound*, referring to whether the
 method was accessed through an instance or a class, respectively.  When a method
-is unbound, its ``im_self`` attribute will be ``None`` and if called, an
+is unbound, its ``__self__`` attribute will be ``None`` and if called, an
 explicit ``self`` object must be passed as the first argument.  In this case,
 ``self`` must be an instance of the unbound method's class (or a subclass of
 that class), otherwise a :exc:`TypeError` is raised.
 
 Like function objects, methods objects support getting arbitrary attributes.
 However, since method attributes are actually stored on the underlying function
-object (``meth.im_func``), setting method attributes on either bound or unbound
+object (``meth.__func__``), setting method attributes on either bound or unbound
 methods is disallowed.  Attempting to set a method attribute results in a
 :exc:`TypeError` being raised.  In order to set a method attribute, you need to
 explicitly set it on the underlying function object::
@@ -2240,7 +2240,7 @@ explicitly set it on the underlying function object::
            pass
 
    c = C()
-   c.method.im_func.whoami = 'my name is c'
+   c.method.__func__.whoami = 'my name is c'
 
 See :ref:`types` for more information.