diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 96e497a3316b..f83999436cbb 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2969,9 +2969,15 @@ def handle_single_axis(
             # Index of largest element < x0 + tol, if any.
             i0 = stickies.searchsorted(x0 + tol) - 1
             x0bound = stickies[i0] if i0 != -1 else None
+            # Ensure the boundary acts only if the sticky is the extreme value
+            if x0bound is not None and x0bound > x0:
+                x0bound = None
             # Index of smallest element > x1 - tol, if any.
             i1 = stickies.searchsorted(x1 - tol)
             x1bound = stickies[i1] if i1 != len(stickies) else None
+            # Ensure the boundary acts only if the sticky is the extreme value
+            if x1bound is not None and x1bound < x1:
+                x1bound = None
 
             # Add the margin in figure space and then transform back, to handle
             # non-linear scales.
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/sticky_tolerance.png b/lib/matplotlib/tests/baseline_images/test_axes/sticky_tolerance.png
new file mode 100644
index 000000000000..a3fb13d0716a
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_axes/sticky_tolerance.png differ
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 0ed5a11c1398..ff4d698fbb6e 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -682,6 +682,25 @@ def test_sticky_shared_axes(fig_test, fig_ref):
     ax0.pcolormesh(Z)
 
 
+@image_comparison(['sticky_tolerance.png'], remove_text=True, style="mpl20")
+def test_sticky_tolerance():
+    fig, axs = plt.subplots(2, 2)
+
+    width = .1
+
+    axs.flat[0].bar(x=0, height=width, bottom=20000.6)
+    axs.flat[0].bar(x=1, height=width, bottom=20000.1)
+
+    axs.flat[1].bar(x=0, height=-width, bottom=20000.6)
+    axs.flat[1].bar(x=1, height=-width, bottom=20000.1)
+
+    axs.flat[2].barh(y=0, width=-width, left=-20000.6)
+    axs.flat[2].barh(y=1, width=-width, left=-20000.1)
+
+    axs.flat[3].barh(y=0, width=width, left=-20000.6)
+    axs.flat[3].barh(y=1, width=width, left=-20000.1)
+
+
 def test_nargs_stem():
     with pytest.raises(TypeError, match='0 were given'):
         # stem() takes 1-3 arguments.