diff --git a/CHANGES.md b/CHANGES.md
index b4e56a1b8..2f790b0dd 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -15,6 +15,9 @@ v0.13.3 (unreleased)
 * Fixed a bug related to callback functions when restoring sessions.
   [#1695]
 
+* Fixed a bug that meant that setting Data.coords after adding
+  components didn't work as expected. [#1196]
+
 * Fixed a Qt-related segmentation fault that occurred during the
   testing process and may also affect users. [#1703]
 
diff --git a/glue/core/data.py b/glue/core/data.py
index ae4bac892..3be0186c9 100644
--- a/glue/core/data.py
+++ b/glue/core/data.py
@@ -72,8 +72,7 @@ def __init__(self, label="", coords=None, **kwargs):
 
         Extra array-like keywords are extracted into components
         """
-        # Coordinate conversion object
-        self.coords = coords or Coordinates()
+
         self._shape = ()
 
         # Components
@@ -83,6 +82,9 @@ def __init__(self, label="", coords=None, **kwargs):
         self._pixel_component_ids = ComponentIDList()
         self._world_component_ids = ComponentIDList()
 
+        # Coordinate conversion object
+        self.coords = coords or Coordinates()
+
         self.id = ComponentIDDict(self)
 
         # Metadata
@@ -113,6 +115,20 @@ def __init__(self, label="", coords=None, **kwargs):
         # uniquely identify them.
         self.uuid = str(uuid.uuid4())
 
+    @property
+    def coords(self):
+        """
+        The coordinates object for the data.
+        """
+        return self._coords
+
+    @coords.setter
+    def coords(self, value):
+        if (hasattr(self, '_coords') and self._coords != value) or not hasattr(self, '_coords'):
+            self._coords = value
+            if len(self.components) > 0:
+                self._update_world_components(self.ndim)
+
     @property
     def subsets(self):
         """
@@ -548,7 +564,10 @@ def add_component_link(self, link, label=None):
         return dc
 
     def _create_pixel_and_world_components(self, ndim):
+        self._update_pixel_components(ndim)
+        self._update_world_components(ndim)
 
+    def _update_pixel_components(self, ndim):
         for i in range(ndim):
             comp = CoordinateComponent(self, i)
             label = pixel_label(i, ndim)
@@ -556,6 +575,10 @@ def _create_pixel_and_world_components(self, ndim):
             self.add_component(comp, cid)
             self._pixel_component_ids.append(cid)
 
+    def _update_world_components(self, ndim):
+        for cid in self._world_component_ids[:]:
+            self.remove_component(cid)
+            self._world_component_ids.remove(cid)
         if self.coords:
             for i in range(ndim):
                 comp = CoordinateComponent(self, i, world=True)
diff --git a/glue/core/tests/test_data.py b/glue/core/tests/test_data.py
index 18a131b04..609c87174 100644
--- a/glue/core/tests/test_data.py
+++ b/glue/core/tests/test_data.py
@@ -4,6 +4,7 @@
 
 import pytest
 import numpy as np
+from numpy.testing import assert_equal
 from mock import MagicMock
 
 from glue.external import six
@@ -14,6 +15,8 @@
 from ..component_link import ComponentLink, CoordinateComponentLink, BinaryComponentLink
 from ..coordinates import Coordinates
 from ..data import Data, pixel_label
+from ..link_helpers import LinkSame
+from ..data_collection import DataCollection
 from ..exceptions import IncompatibleAttribute
 from ..hub import Hub
 from ..registry import Registry
@@ -603,8 +606,6 @@ def test_foreign_pixel_components_not_in_visible():
     """Pixel components from other data should not be visible"""
 
     # currently, this is trivially satisfied since all coordinates are hidden
-    from ..link_helpers import LinkSame
-    from ..data_collection import DataCollection
 
     d1 = Data(x=[1], y=[2])
     d2 = Data(w=[3], v=[4])
@@ -785,3 +786,50 @@ class CustomObject(object):
     assert data2.meta['a'] == 1
     assert data2.meta['b'] == 'test'
     assert 'c' not in data2.meta
+
+
+def test_update_coords():
+
+    # Make sure that when overriding coords, the world coordinate components
+    # are updated.
+
+    data1 = Data(x=[1, 2, 3])
+
+    assert len(data1.components) == 3
+
+    assert_equal(data1[data1.world_component_ids[0]], [0, 1, 2])
+
+    data2 = Data(x=[1, 2, 3])
+
+    assert len(data1.links) == 2
+    assert len(data2.links) == 2
+
+    data_collection = DataCollection([data1, data2])
+
+    assert len(data_collection.links) == 4
+
+    data_collection.add_link(LinkSame(data1.world_component_ids[0], data2.world_component_ids[0]))
+
+    assert len(data_collection.links) == 5
+
+    class CustomCoordinates(Coordinates):
+
+        def axis_label(self, axis):
+            return 'Custom {0}'.format(axis)
+
+        def world2pixel(self, *world):
+            return tuple([0.4 * w for w in world])
+
+        def pixel2world(self, *pixel):
+            return tuple([2.5 * p for p in pixel])
+
+    data1.coords = CustomCoordinates()
+
+    assert len(data1.components) == 3
+
+    assert_equal(data1[data1.world_component_ids[0]], [0, 2.5, 5])
+
+    assert sorted(cid.label for cid in data1.world_component_ids) == ['Custom 0']
+
+    # The link between the two world coordinates should be remove
+    assert len(data_collection.links) == 4
diff --git a/glue/viewers/matplotlib/qt/tests/test_data_viewer.py b/glue/viewers/matplotlib/qt/tests/test_data_viewer.py
index ad0300fbd..ec3491242 100644
--- a/glue/viewers/matplotlib/qt/tests/test_data_viewer.py
+++ b/glue/viewers/matplotlib/qt/tests/test_data_viewer.py
@@ -534,6 +534,7 @@ def test_numerical_data_changed(self):
         self.viewer.add_data(self.data)
         assert self.draw_count == 1
         data = Data(label=self.data.label)
+        data.coords = self.data.coords
         for cid in self.data.visible_components:
             data.add_component(self.data[cid] * 2, cid.label)
         self.data.update_values_from_data(data)