diff --git a/glue_qt/viewers/common/slice_widget.py b/glue_qt/viewers/common/slice_widget.py
index 252c81d7..71f7eaf2 100644
--- a/glue_qt/viewers/common/slice_widget.py
+++ b/glue_qt/viewers/common/slice_widget.py
@@ -114,14 +114,17 @@ def sync_sliders_from_state(self, *args):
                     world_warning = False
                     world_label = self.data.pixel_component_ids[i].label
 
-                slider = SliceWidget(world_label,
-                                     hi=self.data.shape[i] - 1, world=world,
-                                     world_unit=world_unit, world_warning=world_warning)
-
-                self.slider_state = slider.state
-                self.slider_state.add_callback('slice_center', self.sync_state_from_sliders)
-                self._sliders.append(slider)
-                self.layout.addWidget(slider)
+                if self.data.shape[i] > 1:
+                    slider = SliceWidget(world_label,
+                                         hi=self.data.shape[i] - 1, world=world,
+                                         world_unit=world_unit, world_warning=world_warning)
+
+                    self.slider_state = slider.state
+                    self.slider_state.add_callback('slice_center', self.sync_state_from_sliders)
+                    self._sliders.append(slider)
+                    self.layout.addWidget(slider)
+                else:
+                    self._sliders.append(None)
 
         for i in range(self.data.ndim):
             if self._sliders[i] is not None:
diff --git a/glue_qt/viewers/common/tests/test_multi_slice_helper.py b/glue_qt/viewers/common/tests/test_multi_slice_helper.py
new file mode 100644
index 00000000..fe37c599
--- /dev/null
+++ b/glue_qt/viewers/common/tests/test_multi_slice_helper.py
@@ -0,0 +1,33 @@
+from ..data_slice_widget import SliceWidget
+from ..slice_widget import MultiSliceWidgetHelper
+
+from echo import CallbackProperty, HasCallbackProperties
+from glue.core import Data
+from numpy import arange
+from qtpy.QtWidgets import QVBoxLayout
+
+
+class ViewerTestState(HasCallbackProperties):
+    x_att = CallbackProperty()
+    y_att = CallbackProperty()
+    reference_data = CallbackProperty()
+    slices = CallbackProperty()
+
+
+class TestMultiSliceWidgetHelper(object):
+
+    def test_no_slider_if_flat(self):
+        x = arange(72).reshape((6, 4, 1, 3))
+        data = Data(x=x, label="Flat Cube")
+
+        state = ViewerTestState()
+        state.reference_data = data
+        state.x_att = data.pixel_component_ids[0]
+        state.y_att = data.pixel_component_ids[1]
+        state.slices = (0,) * data.ndim
+
+        layout = QVBoxLayout()
+
+        helper = MultiSliceWidgetHelper(viewer_state=state, layout=layout)
+        assert helper._sliders[2] is None
+        assert isinstance(helper._sliders[3], SliceWidget)