diff --git a/glue/viewers/profile/state.py b/glue/viewers/profile/state.py
index bd096693d..cafb59821 100644
--- a/glue/viewers/profile/state.py
+++ b/glue/viewers/profile/state.py
@@ -230,6 +230,13 @@ def _reset_y_limits(self, *event):
                 if y_max > y_min:
                     self.y_min = y_min
                     self.y_max = y_max
+                elif np.allclose(y_min, y_max):
+                    if y_min == 0.0:
+                        dy = np.finfo(y_min).resolution**2
+                    else:
+                        dy = abs(0.1 * y_min)
+                    self.y_min = y_min - dy
+                    self.y_max = y_max + dy
                 else:
                     self.y_min = 0
                     self.y_max = 1
diff --git a/glue/viewers/profile/tests/test_state.py b/glue/viewers/profile/tests/test_state.py
index c574558db..bd89a25d1 100644
--- a/glue/viewers/profile/tests/test_state.py
+++ b/glue/viewers/profile/tests/test_state.py
@@ -1,5 +1,6 @@
 from glue.core.data_collection import DataCollection
 import numpy as np
+import pytest
 
 from numpy.testing import assert_allclose
 
@@ -161,3 +162,22 @@ def test_visible(self):
         x, y = self.layer_state.profile
         assert_allclose(x, [0, 2, 4])
         assert_allclose(y, [3.5, 11.5, 19.5])
+
+
+@pytest.mark.parametrize(('value', 'limits'),
+                         [(0, (-1e-30, 1e-30)),
+                          (1, (0.9, 1.1)),
+                          (-0.1, (-0.11, -0.09))])
+def test_limits_profile_y_constant(value, limits):
+    data = Data(label='d1')
+    data.coords = SimpleCoordinates()
+    data['x'] = np.ones(24).reshape((3, 4, 2)).astype(float) * value
+
+    data_collection = DataCollection([data])
+
+    viewer_state = ProfileViewerState()
+    layer_state = ProfileLayerState(viewer_state=viewer_state, layer=data)
+    viewer_state.layers.append(layer_state)
+    viewer_state.function = 'mean'
+
+    assert_allclose((viewer_state.y_min, viewer_state.y_max), limits)