diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 3c9357106950..f88a04839c75 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -4155,7 +4155,18 @@ def get_default_bbox_extra_artists(self):
         Artists are excluded either by not being visible or
         ``artist.set_in_layout(False)``.
         """
-        return [artist for artist in self.get_children()
+
+        artists = self.get_children()
+        if not (self.axison and self._frameon):
+            # don't do bbox on spines if frame not on.
+            for spine in self.spines.values():
+                artists.remove(spine)
+
+        if not self.axison:
+            for _axis in self._get_axis_list():
+                artists.remove(_axis)
+
+        return [artist for artist in artists
                 if (artist.get_visible() and artist.get_in_layout())]
 
     def get_tightbbox(self, renderer, call_axes_locator=True,
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 211c807eb8c6..45bbb001fc8b 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -125,6 +125,11 @@ def __init__(
 
         self.figure.add_axes(self)
 
+        # mplot3d currently manages its own spines and needs these turned off
+        # for bounding box calculations
+        for k in self.spines.keys():
+            self.spines[k].set_visible(False)
+
     def set_axis_off(self):
         self._axis3don = False
         self.stale = True