diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 4c1032db5..be51c6e38 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1269,6 +1269,7 @@ class MethodDocumenter(DocstringSignatureMixin, ClassLevelDocumenter):  # type:
     Specialized Documenter subclass for methods (normal, static and class).
     """
     objtype = 'method'
+    directivetype = 'method'
     member_order = 50
     priority = 1  # must be more than FunctionDocumenter
 
@@ -1289,16 +1290,11 @@ class MethodDocumenter(DocstringSignatureMixin, ClassLevelDocumenter):  # type:
         if obj is None:
             obj = self.object
 
-        if inspect.isclassmethod(obj):
-            self.directivetype = 'classmethod'
+        if (inspect.isclassmethod(obj) or
+                inspect.isstaticmethod(obj, cls=self.parent, name=self.object_name)):
             # document class and static members before ordinary ones
             self.member_order = self.member_order - 1
-        elif inspect.isstaticmethod(obj, cls=self.parent, name=self.object_name):
-            self.directivetype = 'staticmethod'
-            # document class and static members before ordinary ones
-            self.member_order = self.member_order - 1
-        else:
-            self.directivetype = 'method'
+
         return ret
 
     def format_args(self):
@@ -1314,6 +1310,17 @@ class MethodDocumenter(DocstringSignatureMixin, ClassLevelDocumenter):  # type:
         args = args.replace('\\', '\\\\')
         return args
 
+    def add_directive_header(self, sig):
+        # type: (str) -> None
+        super().add_directive_header(sig)
+
+        sourcename = self.get_sourcename()
+        obj = self.parent.__dict__.get(self.object_name, self.object)
+        if inspect.isclassmethod(obj):
+            self.add_line('   :classmethod:', sourcename)
+        elif inspect.isstaticmethod(obj, cls=self.parent, name=self.object_name):
+            self.add_line('   :staticmethod:', sourcename)
+
     def document_members(self, all_members=False):
         # type: (bool) -> None
         pass
diff --git a/tests/test_autodoc.py b/tests/test_autodoc.py
index 27412a9da..0bf69b74d 100644
--- a/tests/test_autodoc.py
+++ b/tests/test_autodoc.py
@@ -692,9 +692,9 @@ def test_autodoc_members(app):
     actual = do_autodoc(app, 'class', 'target.Base', options)
     assert list(filter(lambda l: '::' in l, actual)) == [
         '.. py:class:: Base',
-        '   .. py:classmethod:: Base.inheritedclassmeth()',
+        '   .. py:method:: Base.inheritedclassmeth()',
         '   .. py:method:: Base.inheritedmeth()',
-        '   .. py:staticmethod:: Base.inheritedstaticmeth(cls)'
+        '   .. py:method:: Base.inheritedstaticmeth(cls)'
     ]
 
     # default specific-members
@@ -703,7 +703,7 @@ def test_autodoc_members(app):
     assert list(filter(lambda l: '::' in l, actual)) == [
         '.. py:class:: Base',
         '   .. py:method:: Base.inheritedmeth()',
-        '   .. py:staticmethod:: Base.inheritedstaticmeth(cls)'
+        '   .. py:method:: Base.inheritedstaticmeth(cls)'
     ]
 
 
@@ -714,7 +714,7 @@ def test_autodoc_exclude_members(app):
     actual = do_autodoc(app, 'class', 'target.Base', options)
     assert list(filter(lambda l: '::' in l, actual)) == [
         '.. py:class:: Base',
-        '   .. py:classmethod:: Base.inheritedclassmeth()'
+        '   .. py:method:: Base.inheritedclassmeth()'
     ]
 
     # members vs exclude-members
@@ -742,9 +742,9 @@ def test_autodoc_undoc_members(app):
         '   .. py:attribute:: Class.inst_attr_string',
         '   .. py:attribute:: Class.mdocattr',
         '   .. py:method:: Class.meth()',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
         '   .. py:attribute:: Class.prop',
-        '   .. py:classmethod:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
+        '   .. py:method:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
         '   .. py:attribute:: Class.skipattr',
         '   .. py:method:: Class.skipmeth()',
         '   .. py:attribute:: Class.udocattr',
@@ -759,11 +759,11 @@ def test_autodoc_inherited_members(app):
     actual = do_autodoc(app, 'class', 'target.Class', options)
     assert list(filter(lambda l: 'method::' in l, actual)) == [
         '   .. py:method:: Class.excludemeth()',
-        '   .. py:classmethod:: Class.inheritedclassmeth()',
+        '   .. py:method:: Class.inheritedclassmeth()',
         '   .. py:method:: Class.inheritedmeth()',
-        '   .. py:staticmethod:: Class.inheritedstaticmeth(cls)',
+        '   .. py:method:: Class.inheritedstaticmeth(cls)',
         '   .. py:method:: Class.meth()',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
         '   .. py:method:: Class.skipmeth()'
     ]
 
@@ -822,9 +822,9 @@ def test_autodoc_special_members(app):
         '   .. py:attribute:: Class.inst_attr_string',
         '   .. py:attribute:: Class.mdocattr',
         '   .. py:method:: Class.meth()',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
         '   .. py:attribute:: Class.prop',
-        '   .. py:classmethod:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
+        '   .. py:method:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
         '   .. py:attribute:: Class.skipattr',
         '   .. py:method:: Class.skipmeth()',
         '   .. py:attribute:: Class.udocattr',
@@ -942,6 +942,34 @@ def test_autodoc_inner_class(app):
     ]
 
 
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_autodoc_classmethod(app):
+    actual = do_autodoc(app, 'method', 'target.Base.inheritedclassmeth')
+    assert list(actual) == [
+        '',
+        '.. py:method:: Base.inheritedclassmeth()',
+        '   :module: target',
+        '   :classmethod:',
+        '',
+        '   Inherited class method.',
+        '   '
+    ]
+
+
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_autodoc_staticmethod(app):
+    actual = do_autodoc(app, 'method', 'target.Base.inheritedstaticmeth')
+    assert list(actual) == [
+        '',
+        '.. py:method:: Base.inheritedstaticmeth(cls)',
+        '   :module: target',
+        '   :staticmethod:',
+        '',
+        '   Inherited static method.',
+        '   '
+    ]
+
+
 @pytest.mark.sphinx('html', testroot='ext-autodoc')
 def test_autodoc_descriptor(app):
     actual = do_autodoc(app, 'attribute', 'target.Class.descr')
@@ -991,8 +1019,8 @@ def test_autodoc_member_order(app):
         '   .. py:attribute:: Class.docattr',
         '   .. py:attribute:: Class.udocattr',
         '   .. py:attribute:: Class.mdocattr',
-        '   .. py:classmethod:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
         '   .. py:attribute:: Class.inst_attr_inline',
         '   .. py:attribute:: Class.inst_attr_comment',
         '   .. py:attribute:: Class.inst_attr_string',
@@ -1009,8 +1037,8 @@ def test_autodoc_member_order(app):
         '.. py:class:: Class(arg)',
         '   .. py:method:: Class.excludemeth()',
         '   .. py:method:: Class.meth()',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
-        '   .. py:classmethod:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
         '   .. py:method:: Class.skipmeth()',
         '   .. py:method:: Class.undocmeth()',
         '   .. py:attribute:: Class._private_inst_attr',
@@ -1043,9 +1071,9 @@ def test_autodoc_member_order(app):
         '   .. py:attribute:: Class.inst_attr_string',
         '   .. py:attribute:: Class.mdocattr',
         '   .. py:method:: Class.meth()',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
         '   .. py:attribute:: Class.prop',
-        '   .. py:classmethod:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
+        '   .. py:method:: Class.roger(a, *, b=2, c=3, d=4, e=5, f=6)',
         '   .. py:attribute:: Class.skipattr',
         '   .. py:method:: Class.skipmeth()',
         '   .. py:attribute:: Class.udocattr',
@@ -1642,7 +1670,7 @@ def test_autodoc_default_options_with_values(app):
         '   .. py:attribute:: Class.docattr',
         '   .. py:attribute:: Class.udocattr',
         '   .. py:attribute:: Class.mdocattr',
-        '   .. py:classmethod:: Class.moore(a, e, f) -> happiness',
+        '   .. py:method:: Class.moore(a, e, f) -> happiness',
         '   .. py:attribute:: Class.inst_attr_inline',
         '   .. py:attribute:: Class.inst_attr_comment',
         '   .. py:attribute:: Class.inst_attr_string',