diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 423891b3e972..3619aeb0249a 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -74,7 +74,7 @@ def test_basic(self):
         ax.minorticks_on()
         test_value = np.array([0.05, 0.1, 0.15, 0.25, 0.3, 0.35, 0.45,
                                0.5, 0.55, 0.65, 0.7, 0.75, 0.85, 0.9,
-                               0.95, 1, 1.05, 1.1, 1.15, 1.25, 1.3, 1.35])
+                               0.95, 1.05, 1.1, 1.15, 1.25, 1.3, 1.35])
         assert_almost_equal(ax.xaxis.get_ticklocs(minor=True), test_value)
 
     # NB: the following values are assuming that *xlim* is [0, 5]
@@ -97,6 +97,53 @@ def test_low_number_of_majorticks(
         ax.xaxis.set_minor_locator(mticker.AutoMinorLocator())
         assert len(ax.xaxis.get_minorticklocs()) == expected_nb_minorticks
 
+    limits = [(0, 1.39), (0, 0.139),
+              (0, 0.11e-19), (0, 0.112e-12),
+              (-2.0e-07, -3.3e-08), (1.20e-06, 1.42e-06),
+              (-1.34e-06, -1.44e-06), (-8.76e-07, -1.51e-06)]
+
+    reference = [
+        [0.05, 0.1, 0.15, 0.25, 0.3, 0.35, 0.45, 0.5, 0.55, 0.65, 0.7,
+         0.75, 0.85, 0.9, 0.95, 1.05, 1.1, 1.15, 1.25, 1.3, 1.35],
+        [0.005, 0.01, 0.015, 0.025, 0.03, 0.035, 0.045, 0.05, 0.055, 0.065,
+         0.07, 0.075, 0.085, 0.09, 0.095, 0.105, 0.11, 0.115, 0.125, 0.13,
+         0.135],
+        [5.00e-22, 1.00e-21, 1.50e-21, 2.50e-21, 3.00e-21, 3.50e-21, 4.50e-21,
+         5.00e-21, 5.50e-21, 6.50e-21, 7.00e-21, 7.50e-21, 8.50e-21, 9.00e-21,
+         9.50e-21, 1.05e-20, 1.10e-20],
+        [5.00e-15, 1.00e-14, 1.50e-14, 2.50e-14, 3.00e-14, 3.50e-14, 4.50e-14,
+         5.00e-14, 5.50e-14, 6.50e-14, 7.00e-14, 7.50e-14, 8.50e-14, 9.00e-14,
+         9.50e-14, 1.05e-13, 1.10e-13],
+        [-1.95e-07, -1.90e-07, -1.85e-07, -1.75e-07, -1.70e-07, -1.65e-07,
+         -1.55e-07, -1.50e-07, -1.45e-07, -1.35e-07, -1.30e-07, -1.25e-07,
+         -1.15e-07, -1.10e-07, -1.05e-07, -9.50e-08, -9.00e-08, -8.50e-08,
+         -7.50e-08, -7.00e-08, -6.50e-08, -5.50e-08, -5.00e-08, -4.50e-08,
+         -3.50e-08],
+        [1.21e-06, 1.22e-06, 1.23e-06, 1.24e-06, 1.26e-06, 1.27e-06, 1.28e-06,
+         1.29e-06, 1.31e-06, 1.32e-06, 1.33e-06, 1.34e-06, 1.36e-06, 1.37e-06,
+         1.38e-06, 1.39e-06, 1.41e-06, 1.42e-06],
+        [-1.435e-06, -1.430e-06, -1.425e-06, -1.415e-06, -1.410e-06,
+         -1.405e-06, -1.395e-06, -1.390e-06, -1.385e-06, -1.375e-06,
+         -1.370e-06, -1.365e-06, -1.355e-06, -1.350e-06, -1.345e-06],
+        [-1.48e-06, -1.46e-06, -1.44e-06, -1.42e-06, -1.38e-06, -1.36e-06,
+         -1.34e-06, -1.32e-06, -1.28e-06, -1.26e-06, -1.24e-06, -1.22e-06,
+         -1.18e-06, -1.16e-06, -1.14e-06, -1.12e-06, -1.08e-06, -1.06e-06,
+         -1.04e-06, -1.02e-06, -9.80e-07, -9.60e-07, -9.40e-07, -9.20e-07,
+         -8.80e-07]]
+
+    additional_data = list(zip(limits, reference))
+
+    @pytest.mark.parametrize('lim, ref', additional_data)
+    def test_additional(self, lim, ref):
+        fig, ax = plt.subplots()
+
+        ax.minorticks_on()
+        ax.grid(True, 'minor', 'y', linewidth=1)
+        ax.grid(True, 'major', color='k', linewidth=1)
+        ax.set_ylim(lim)
+
+        assert_almost_equal(ax.yaxis.get_ticklocs(minor=True), ref)
+
 
 class TestLogLocator(object):
     def test_basic(self):
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index abac4392dca6..cc3b227bb293 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -2535,8 +2535,10 @@ def __call__(self):
         tmin = ((vmin - t0) // minorstep + 1) * minorstep
         tmax = ((vmax - t0) // minorstep + 1) * minorstep
         locs = np.arange(tmin, tmax, minorstep) + t0
-        cond = np.abs((locs - t0) % majorstep) > minorstep / 10.0
-        locs = locs.compress(cond)
+        mod = np.abs((locs - t0) % majorstep)
+        cond1 = mod > minorstep / 10.0
+        cond2 = ~np.isclose(mod, majorstep, atol=0)
+        locs = locs.compress(cond1 & cond2)
 
         return self.raise_if_exceeds(np.array(locs))