diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 191afa0b9950..165f8b8c81e4 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -1,5 +1,6 @@
 import warnings
 import re
+import itertools
 
 import numpy as np
 from numpy.testing import assert_almost_equal, assert_array_equal
@@ -366,6 +367,44 @@ def test_minor_attr(self):
         loc.set_params(minor=False)
         assert not loc.minor
 
+    acceptable_vmin_vmax = [
+        *(2.5 ** np.arange(-3, 0)),
+        *(1 - 2.5 ** np.arange(-3, 0)),
+    ]
+
+    @pytest.mark.parametrize(
+        "lims",
+        [
+            (a, b)
+            for (a, b) in itertools.product(acceptable_vmin_vmax, repeat=2)
+            if a != b
+        ],
+    )
+    def test_nonsingular_ok(self, lims):
+        """
+        Create logit locator, and test the nonsingular method for acceptable
+        value
+        """
+        loc = mticker.LogitLocator()
+        lims2 = loc.nonsingular(*lims)
+        assert sorted(lims) == sorted(lims2)
+
+    @pytest.mark.parametrize("okval", acceptable_vmin_vmax)
+    def test_nonsingular_nok(self, okval):
+        """
+        Create logit locator, and test the nonsingular method for non
+        acceptable value
+        """
+        loc = mticker.LogitLocator()
+        vmin, vmax = (-1, okval)
+        vmin2, vmax2 = loc.nonsingular(vmin, vmax)
+        assert vmax2 == vmax
+        assert 0 < vmin2 < vmax2
+        vmin, vmax = (okval, 2)
+        vmin2, vmax2 = loc.nonsingular(vmin, vmax)
+        assert vmin2 == vmin
+        assert vmin2 < vmax2 < 1
+
 
 class TestFixedLocator:
     def test_set_params(self):
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index 16e8e02b2c5d..1aacec42941b 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -2792,32 +2792,38 @@ def ideal_ticks(x):
         return MaxNLocator.tick_values(self, vmin, vmax)
 
     def nonsingular(self, vmin, vmax):
-        initial_range = (1e-7, 1 - 1e-7)
-        if not np.isfinite(vmin) or not np.isfinite(vmax):
-            return initial_range  # no data plotted yet
-
+        standard_minpos = 1e-7
+        initial_range = (standard_minpos, 1 - standard_minpos)
         if vmin > vmax:
             vmin, vmax = vmax, vmin
-
-        # what to do if a window beyond ]0, 1[ is chosen
-        if self.axis is not None:
-            minpos = self.axis.get_minpos()
-            if not np.isfinite(minpos):
-                return initial_range  # again, no data plotted
+        if not np.isfinite(vmin) or not np.isfinite(vmax):
+            vmin, vmax = initial_range  # Initial range, no data plotted yet.
+        elif vmax <= 0 or vmin >= 1:
+            # vmax <= 0 occurs when all values are negative
+            # vmin >= 1 occurs when all values are greater than one
+            cbook._warn_external(
+                "Data has no values between 0 and 1, and therefore cannot be "
+                "logit-scaled."
+            )
+            vmin, vmax = initial_range
         else:
-            minpos = 1e-7  # should not occur in normal use
-
-        # NOTE: for vmax, we should query a property similar to get_minpos, but
-        # related to the maximal, less-than-one data point. Unfortunately,
-        # Bbox._minpos is defined very deep in the BBox and updated with data,
-        # so for now we use 1 - minpos as a substitute.
-
-        if vmin <= 0:
-            vmin = minpos
-        if vmax >= 1:
-            vmax = 1 - minpos
-        if vmin == vmax:
-            return 0.1 * vmin, 1 - 0.1 * vmin
+            minpos = (
+                self.axis.get_minpos()
+                if self.axis is not None
+                else standard_minpos
+            )
+            if not np.isfinite(minpos):
+                minpos = standard_minpos  # This should never take effect.
+            if vmin <= 0:
+                vmin = minpos
+            # NOTE: for vmax, we should query a property similar to get_minpos,
+            # but related to the maximal, less-than-one data point.
+            # Unfortunately, Bbox._minpos is defined very deep in the BBox and
+            # updated with data, so for now we use 1 - minpos as a substitute.
+            if vmax >= 1:
+                vmax = 1 - minpos
+            if vmin == vmax:
+                vmin, vmax = 0.1 * vmin, 1 - 0.1 * vmin
 
         return vmin, vmax