diff --git a/lib/matplotlib/_api/deprecation.py b/lib/matplotlib/_api/deprecation.py
index 7c3a17965928..1487e30e504d 100644
--- a/lib/matplotlib/_api/deprecation.py
+++ b/lib/matplotlib/_api/deprecation.py
@@ -273,7 +273,7 @@ def wrapper(*args, **kwargs):
 
 class deprecate_privatize_attribute:
     """
-    Helper to deprecate public access to an attribute.
+    Helper to deprecate public access to an attribute (or method).
 
     This helper should only be used at class scope, as follows::
 
@@ -283,7 +283,8 @@ class Foo:
     where *all* parameters are forwarded to `deprecated`.  This form makes
     ``attr`` a property which forwards access to ``self._attr`` (same name but
     with a leading underscore), with a deprecation warning.  Note that the
-    attribute name is derived from *the name this helper is assigned to*.
+    attribute name is derived from *the name this helper is assigned to*.  This
+    helper also works for deprecating methods.
     """
 
     def __init__(self, *args, **kwargs):
diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index 32e069ed69cf..6417d30178c0 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -3264,11 +3264,6 @@ def push_current(self):
                  for ax in self.canvas.figure.axes}))
         self.set_history_buttons()
 
-    @_api.deprecated("3.3", alternative="toolbar.canvas.draw_idle()")
-    def draw(self):
-        """Redraw the canvases, update the locators."""
-        self._draw()
-
     # Can be removed once Locator.refresh() is removed, and replaced by an
     # inline call to self.canvas.draw_idle().
     def _draw(self):
@@ -3287,6 +3282,9 @@ def _draw(self):
                 mpl.ticker._if_refresh_overridden_call_and_emit_deprec(loc)
         self.canvas.draw_idle()
 
+    draw = _api.deprecate_privatize_attribute(
+        "3.3", alternative="toolbar.canvas.draw_idle()")
+
     def _update_view(self):
         """
         Update the viewlim and position from the view and position stack for
diff --git a/lib/matplotlib/backend_tools.py b/lib/matplotlib/backend_tools.py
index a8bad1edab5a..2fa598aa2626 100644
--- a/lib/matplotlib/backend_tools.py
+++ b/lib/matplotlib/backend_tools.py
@@ -613,11 +613,6 @@ def update_home_views(self, figure=None):
             if a not in self.home_views[figure]:
                 self.home_views[figure][a] = a._get_view()
 
-    @_api.deprecated("3.3", alternative="self.figure.canvas.draw_idle()")
-    def refresh_locators(self):
-        """Redraw the canvases, update the locators."""
-        self._refresh_locators()
-
     # Can be removed once Locator.refresh() is removed, and replaced by an
     # inline call to self.figure.canvas.draw_idle().
     def _refresh_locators(self):
@@ -640,6 +635,9 @@ def _refresh_locators(self):
                 mpl.ticker._if_refresh_overridden_call_and_emit_deprec(loc)
         self.figure.canvas.draw_idle()
 
+    refresh_locators = _api.deprecate_privatize_attribute(
+        "3.3", alternative="self.figure.canvas.draw_idle()")
+
     def home(self):
         """Recall the first view and position from the stack."""
         self.views[self.figure].home()
diff --git a/lib/matplotlib/cm.py b/lib/matplotlib/cm.py
index 376d703da13f..667aed880efd 100644
--- a/lib/matplotlib/cm.py
+++ b/lib/matplotlib/cm.py
@@ -501,11 +501,5 @@ def changed(self):
         self.stale = True
 
     update_dict = _api.deprecate_privatize_attribute("3.3")
-
-    @_api.deprecated("3.3")
-    def add_checker(self, checker):
-        return self._add_checker(checker)
-
-    @_api.deprecated("3.3")
-    def check_update(self, checker):
-        return self._check_update(checker)
+    add_checker = _api.deprecate_privatize_attribute("3.3")
+    check_update = _api.deprecate_privatize_attribute("3.3")
diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index 31d9b6176821..788fdb66b9af 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -546,10 +546,6 @@ def draw_all(self):
         if self.filled:
             self._add_solids(X, Y, self._values[:, np.newaxis])
 
-    @_api.deprecated("3.3")
-    def config_axis(self):
-        self._config_axis()
-
     def _config_axis(self):
         """Set up long and short axis."""
         ax = self.ax
@@ -567,6 +563,8 @@ def _config_axis(self):
         short_axis.set_ticks([], minor=True)
         self.stale = True
 
+    config_axis = _api.deprecate_privatize_attribute("3.3")
+
     def _get_ticker_locator_formatter(self):
         """
         Return the ``locator`` and ``formatter`` of the colorbar.
diff --git a/lib/matplotlib/tests/test_api.py b/lib/matplotlib/tests/test_api.py
index 29ca4caf5ca0..43fbb2f2bc8a 100644
--- a/lib/matplotlib/tests/test_api.py
+++ b/lib/matplotlib/tests/test_api.py
@@ -34,6 +34,19 @@ def f(cls):
         a.f
 
 
+def test_deprecate_privatize_attribute():
+    class C:
+        def __init__(self): self._attr = 1
+        def _meth(self, arg): pass
+        attr = _api.deprecate_privatize_attribute("0.0")
+        meth = _api.deprecate_privatize_attribute("0.0")
+
+    with pytest.warns(_api.MatplotlibDeprecationWarning):
+        C().attr
+    with pytest.warns(_api.MatplotlibDeprecationWarning):
+        C().meth(42)
+
+
 def test_delete_parameter():
     @_api.delete_parameter("3.0", "foo")
     def func1(foo=None):