matplotlib
diff --git a/‎doc/api/next_api_changes/behaviour.rst
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diff --git a/‎lib/matplotlib/axis.py
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diff --git a/‎lib/matplotlib/tests/test_axes.py
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@@ -133,3 +133,8 @@ using :rc:`keymap.quit_all`.
 Autoscale for arrow
 ~~~~~~~~~~~~~~~~~~~
 Calling ax.arrow() will now autoscale the axes.
+
+``set_tick_params(label1On=False)`` now also makes the offset text (if any) invisible
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+... because the offset text can rarely be interpreted without tick labels
+anyways.
@@ -824,7 +824,11 @@ def set_tick_params(self, which='major', reset=False, **kw):
                 self._minor_tick_kw.update(kwtrans)
                 for tick in self.minorTicks:
                     tick._apply_params(**kwtrans)
-            # special-case label color to also apply to the offset text
+            # labelOn and labelcolor also apply to the offset text.
+            if 'label1On' in kwtrans or 'label2On' in kwtrans:
+                self.offsetText.set_visible(
+                    self._major_tick_kw.get('label1On', False)
+                    or self._major_tick_kw.get('label2On', False))
             if 'labelcolor' in kwtrans:
                 self.offsetText.set_color(kwtrans['labelcolor'])
 
 
@@ -5497,6 +5497,16 @@ def test_offset_label_color():
     assert ax.yaxis.get_offset_text().get_color() == 'red'
 
 
+def test_offset_text_visible():
+    fig = plt.figure()
+    ax = fig.add_subplot(1, 1, 1)
+    ax.plot([1.01e9, 1.02e9, 1.03e9])
+    ax.yaxis.set_tick_params(label1On=False, label2On=True)
+    assert ax.yaxis.get_offset_text().get_visible()
+    ax.yaxis.set_tick_params(label2On=False)
+    assert not ax.yaxis.get_offset_text().get_visible()
+
+
 def test_large_offset():
     fig, ax = plt.subplots()
     ax.plot((1 + np.array([0, 1.e-12])) * 1.e27)