diff --git a/lib/matplotlib/artist.py b/lib/matplotlib/artist.py
index 44df8f8c0704..5c3f6dc5952f 100644
--- a/lib/matplotlib/artist.py
+++ b/lib/matplotlib/artist.py
@@ -353,7 +353,7 @@ def get_tightbbox(self, renderer=None):
 
         Parameters
         ----------
-        renderer : `.RendererBase` subclass
+        renderer : `~matplotlib.backend_bases.RendererBase` subclass, optional
             renderer that will be used to draw the figures (i.e.
             ``fig.canvas.get_renderer()``)
 
@@ -440,7 +440,7 @@ def set_transform(self, t):
 
         Parameters
         ----------
-        t : `.Transform`
+        t : `~matplotlib.transforms.Transform`
         """
         self._transform = t
         self._transformSet = True
@@ -733,7 +733,7 @@ def set_figure(self, fig):
 
         Parameters
         ----------
-        fig : `.Figure`
+        fig : `~matplotlib.figure.Figure`
         """
         # if this is a no-op just return
         if self.figure is fig:
@@ -757,15 +757,16 @@ def set_clip_box(self, clipbox):
 
         Parameters
         ----------
-        clipbox : `.BboxBase` or None
-            Typically would be created from a `.TransformedBbox`. For
-            instance ``TransformedBbox(Bbox([[0, 0], [1, 1]]), ax.transAxes)``
-            is the default clipping for an artist added to an Axes.
+        clipbox : `~matplotlib.transforms.BboxBase` or None
+            Will typically be created from a `.TransformedBbox`. For instance,
+            ``TransformedBbox(Bbox([[0, 0], [1, 1]]), ax.transAxes)`` is the default
+            clipping for an artist added to an Axes.
 
         """
-        self.clipbox = clipbox
-        self.pchanged()
-        self.stale = True
+        if clipbox != self.clipbox:
+            self.clipbox = clipbox
+            self.pchanged()
+            self.stale = True
 
     def set_clip_path(self, path, transform=None):
         """
@@ -986,7 +987,7 @@ def draw(self, renderer):
 
         Parameters
         ----------
-        renderer : `.RendererBase` subclass.
+        renderer : `~matplotlib.backend_bases.RendererBase` subclass.
 
         Notes
         -----
@@ -1010,9 +1011,10 @@ def set_alpha(self, alpha):
                 f'alpha must be numeric or None, not {type(alpha)}')
         if alpha is not None and not (0 <= alpha <= 1):
             raise ValueError(f'alpha ({alpha}) is outside 0-1 range')
-        self._alpha = alpha
-        self.pchanged()
-        self.stale = True
+        if alpha != self._alpha:
+            self._alpha = alpha
+            self.pchanged()
+            self.stale = True
 
     def _set_alpha_for_array(self, alpha):
         """
@@ -1045,9 +1047,10 @@ def set_visible(self, b):
         ----------
         b : bool
         """
-        self._visible = b
-        self.pchanged()
-        self.stale = True
+        if b != self._visible:
+            self._visible = b
+            self.pchanged()
+            self.stale = True
 
     def set_animated(self, b):
         """
@@ -1095,9 +1098,11 @@ def set_label(self, s):
         s : object
             *s* will be converted to a string by calling `str`.
         """
-        self._label = str(s) if s is not None else None
-        self.pchanged()
-        self.stale = True
+        label = str(s) if s is not None else None
+        if label != self._label:
+            self._label = label
+            self.pchanged()
+            self.stale = True
 
     def get_zorder(self):
         """Return the artist's zorder."""
@@ -1114,9 +1119,10 @@ def set_zorder(self, level):
         """
         if level is None:
             level = self.__class__.zorder
-        self.zorder = level
-        self.pchanged()
-        self.stale = True
+        if level != self.zorder:
+            self.zorder = level
+            self.pchanged()
+            self.stale = True
 
     @property
     def sticky_edges(self):
diff --git a/lib/matplotlib/container.py b/lib/matplotlib/container.py
index 62fe9a35e666..e11fea391871 100644
--- a/lib/matplotlib/container.py
+++ b/lib/matplotlib/container.py
@@ -19,7 +19,7 @@ def __new__(cls, *args, **kwargs):
     def __init__(self, kl, label=None):
         self._callbacks = cbook.CallbackRegistry(signals=["pchanged"])
         self._remove_method = None
-        self.set_label(label)
+        self._label = label
 
     def remove(self):
         for c in cbook.flatten(