diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 97815c09eb9..12a505fdab8 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -2234,6 +2234,12 @@ def dummy():
             return None
 
     def get_doc(self, ignore: int = None) -> Optional[List[List[str]]]:
+        if self._new_docstrings is not None:
+            # docstring already returned previously, then modified by
+            # `DocstringSignatureMixin`.  Just return the previously-computed
+            # result, so that we don't lose the processing done by
+            # `DocstringSignatureMixin`.
+            return self._new_docstrings
         if self.objpath[-1] == '__init__':
             docstring = getdoc(self.object, self.get_attr,
                                self.config.autodoc_inherit_docstrings,
@@ -2248,15 +2254,13 @@ def get_doc(self, ignore: int = None) -> Optional[List[List[str]]]:
             else:
                 return []
         elif self.objpath[-1] == '__new__':
-            __new__ = self.get_attr(self.object, '__new__', None)
-            if __new__:
-                docstring = getdoc(__new__, self.get_attr,
-                                   self.config.autodoc_inherit_docstrings,
-                                   self.parent, self.object_name)
-                if (docstring is not None and
-                    (docstring == object.__new__.__doc__ or  # for pypy
-                     docstring.strip() == object.__new__.__doc__)):  # for !pypy
-                    docstring = None
+            docstring = getdoc(self.object, self.get_attr,
+                               self.config.autodoc_inherit_docstrings,
+                               self.parent, self.object_name)
+            if (docstring is not None and
+                (docstring == object.__new__.__doc__ or  # for pypy
+                 docstring.strip() == object.__new__.__doc__)):  # for !pypy
+                docstring = None
             if docstring:
                 tab_width = self.directive.state.document.settings.tab_width
                 return [prepare_docstring(docstring, tabsize=tab_width)]
diff --git a/tests/roots/test-ext-autodoc/target/__init__.py b/tests/roots/test-ext-autodoc/target/__init__.py
index e49f9a14104..54f52bbffbd 100644
--- a/tests/roots/test-ext-autodoc/target/__init__.py
+++ b/tests/roots/test-ext-autodoc/target/__init__.py
@@ -114,6 +114,20 @@ class InnerChild(Outer.Inner):
 
 
 class DocstringSig(object):
+    def __new__(cls, *new_args, **new_kwargs):
+        """__new__(cls, d, e=1) -> DocstringSig
+First line of docstring
+
+        rest of docstring
+        """
+
+    def __init__(self, *init_args, **init_kwargs):
+        """__init__(self, a, b=1) -> None
+First line of docstring
+
+        rest of docstring
+        """
+
     def meth(self):
         """meth(FOO, BAR=1) -> BAZ
 First line of docstring
diff --git a/tests/test_ext_autodoc_configs.py b/tests/test_ext_autodoc_configs.py
index 0f058040437..6e0159d1448 100644
--- a/tests/test_ext_autodoc_configs.py
+++ b/tests/test_ext_autodoc_configs.py
@@ -287,14 +287,34 @@ def test_autodoc_inherit_docstrings(app):
 
 @pytest.mark.sphinx('html', testroot='ext-autodoc')
 def test_autodoc_docstring_signature(app):
-    options = {"members": None}
+    options = {"members": None, "special-members": "__init__, __new__"}
     actual = do_autodoc(app, 'class', 'target.DocstringSig', options)
     assert list(actual) == [
         '',
-        '.. py:class:: DocstringSig()',
+        # FIXME: Ideally this would instead be: `DocstringSig(d, e=1)` but
+        # currently `ClassDocumenter` does not apply the docstring signature
+        # logic when extracting a signature from a __new__ or __init__ method.
+        '.. py:class:: DocstringSig(*new_args, **new_kwargs)',
         '   :module: target',
         '',
         '',
+        '   .. py:method:: DocstringSig.__init__(self, a, b=1) -> None',
+        '      :module: target',
+        '',
+        '      First line of docstring',
+        '',
+        '      rest of docstring',
+        '',
+        '',
+        '   .. py:method:: DocstringSig.__new__(cls, d, e=1) -> DocstringSig',
+        '      :module: target',
+        '      :staticmethod:',
+        '',
+        '      First line of docstring',
+        '',
+        '      rest of docstring',
+        '',
+        '',
         '   .. py:method:: DocstringSig.meth(FOO, BAR=1) -> BAZ',
         '      :module: target',
         '',
@@ -331,10 +351,31 @@ def test_autodoc_docstring_signature(app):
     actual = do_autodoc(app, 'class', 'target.DocstringSig', options)
     assert list(actual) == [
         '',
-        '.. py:class:: DocstringSig()',
+        '.. py:class:: DocstringSig(*new_args, **new_kwargs)',
         '   :module: target',
         '',
         '',
+        '   .. py:method:: DocstringSig.__init__(*init_args, **init_kwargs)',
+        '      :module: target',
+        '',
+        '      __init__(self, a, b=1) -> None',
+        '      First line of docstring',
+        '',
+        '              rest of docstring',
+        '',
+        '',
+        '',
+        '   .. py:method:: DocstringSig.__new__(cls, *new_args, **new_kwargs)',
+        '      :module: target',
+        '      :staticmethod:',
+        '',
+        '      __new__(cls, d, e=1) -> DocstringSig',
+        '      First line of docstring',
+        '',
+        '              rest of docstring',
+        '',
+        '',
+        '',
         '   .. py:method:: DocstringSig.meth()',
         '      :module: target',
         '',