diff --git a/doc/api/next_api_changes/behavior/26307-AL.rst b/doc/api/next_api_changes/behavior/26307-AL.rst
new file mode 100644
index 000000000000..a83366f012b3
--- /dev/null
+++ b/doc/api/next_api_changes/behavior/26307-AL.rst
@@ -0,0 +1,4 @@
+Colorbars of single-value norms now map that value to the lowest color, not the midpoint color
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+This behavior is consistent with e.g. how `~.Axes.imshow` handle inputs with
+``vmin == vmax``.
diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index af61e4671ff4..5539f818d909 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -1088,8 +1088,13 @@ def _process_values(self):
             # If we still aren't scaled after autoscaling, use 0, 1 as default
             self.norm.vmin = 0
             self.norm.vmax = 1
-        self.norm.vmin, self.norm.vmax = mtransforms.nonsingular(
-            self.norm.vmin, self.norm.vmax, expander=0.1)
+
+        # Only expand vmax if needed, to match Normalize's behavior of mapping
+        # everything to 0 if the norm is singular.
+        vmin, vmax = sorted([self.norm.vmin, self.norm.vmax])
+        self.norm.vmin = vmin
+        _, self.norm.vmax = mtransforms.nonsingular(vmin, vmax, expander=0.1)
+
         if (not isinstance(self.norm, colors.BoundaryNorm) and
                 (self.boundaries is None)):
             b = self.norm.inverse(b)
diff --git a/lib/matplotlib/tests/baseline_images/test_colorbar/colorbar_single_scatter.png b/lib/matplotlib/tests/baseline_images/test_colorbar/colorbar_single_scatter.png
deleted file mode 100644
index 18d9cf02add0..000000000000
Binary files a/lib/matplotlib/tests/baseline_images/test_colorbar/colorbar_single_scatter.png and /dev/null differ
diff --git a/lib/matplotlib/tests/test_colorbar.py b/lib/matplotlib/tests/test_colorbar.py
index 74742d8c2369..a1929bfb6daf 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -265,18 +265,17 @@ def test_gridspec_make_colorbar():
     plt.subplots_adjust(top=0.95, right=0.95, bottom=0.2, hspace=0.25)
 
 
-@image_comparison(['colorbar_single_scatter.png'], remove_text=True,
-                  savefig_kwarg={'dpi': 40})
 def test_colorbar_single_scatter():
-    # Issue #2642: if a path collection has only one entry,
-    # the norm scaling within the colorbar must ensure a
-    # finite range, otherwise a zero denominator will occur in _locate.
+    # Issue #2642:  If a path collection has only one entry, the norm scaling within the
+    # colorbar must ensure a finite range, otherwise a zero denominator will occur in
+    # _locate.  Also, adding the colorbar must not change the value's normalization.
     plt.figure()
-    x = y = [0]
-    z = [50]
-    cmap = mpl.colormaps['jet'].resampled(16)
-    cs = plt.scatter(x, y, z, c=z, cmap=cmap)
+    v = 50
+    cs = plt.scatter([0], [0], c=[50])
+    old_normed = cs.norm(v)
     plt.colorbar(cs)
+    new_normed = cs.norm(v)
+    assert old_normed == new_normed
 
 
 @pytest.mark.parametrize('use_gridspec', [True, False])