diff --git a/ndcube/ndcube.py b/ndcube/ndcube.py
index bf3eb2161..93bdf5659 100644
--- a/ndcube/ndcube.py
+++ b/ndcube/ndcube.py
@@ -1160,10 +1160,11 @@ def my_propagate(uncertainty, data, mask, **kwargs):
         if propagate_uncertainties:
             if self.uncertainty is None:
                 warnings.warn("Uncertainties cannot be propagated as there are no uncertainties, "
-                              "i.e. self.uncertainty is None.")
+                              "i.e., the `uncertainty` keyword was never set on creation of this NDCube.")
             elif isinstance(self.uncertainty, astropy.nddata.UnknownUncertainty):
-                warnings.warn("Uncertainty is an UnknownUncertainty which does not "
-                              "support uncertainty propagation.")
+                warnings.warn("The uncertainty on this NDCube has no known way to propagate forward and so will be dropped. "
+                              "To create an uncertainty that can propagate, please see "
+                              "https://docs.astropy.org/en/stable/uncertainty/index.html")
             elif (not operation_ignores_mask
                   and (self.mask is True or (self.mask is not None
                                              and not isinstance(self.mask, bool)
diff --git a/ndcube/tests/test_ndcube.py b/ndcube/tests/test_ndcube.py
index f9708d3b7..eb08bd07c 100644
--- a/ndcube/tests/test_ndcube.py
+++ b/ndcube/tests/test_ndcube.py
@@ -790,7 +790,7 @@ def test_wcs_type_after_init(ndcube_3d_ln_lt_l, wcs_3d_l_lt_ln):
 def test_rebin(ndcube_3d_l_ln_lt_ectime):
     cube = ndcube_3d_l_ln_lt_ectime[:, 1:]
     bin_shape = (10, 2, 1)
-    with pytest.warns(UserWarning, match="Uncertainty is an UnknownUncertainty which does not support uncertainty propagation."):
+    with pytest.warns(UserWarning, match="The uncertainty on this NDCube has no known way to propagate forward"):
         output = cube.rebin(bin_shape, operation=np.sum, propagate_uncertainties=True)
     output_sc, output_spec = output.axis_world_coords(wcs=output.wcs)
     output_time, = output.axis_world_coords(wcs=output.extra_coords)
@@ -845,7 +845,7 @@ def test_rebin_no_ec(ndcube_3d_l_ln_lt_ectime):
     cube = ndcube_3d_l_ln_lt_ectime[:, 1:]
     cube._extra_coords = ExtraCoords(cube)
     bin_shape = (10, 2, 1)
-    with pytest.warns(UserWarning, match="Uncertainty is an UnknownUncertainty which does not support uncertainty propagation."):
+    with pytest.warns(UserWarning, match="The uncertainty on this NDCube has no known way to propagate forward"):
         output = cube.rebin(bin_shape, operation=np.mean, propagate_uncertainties=True)
     assert output.extra_coords.is_empty
 
@@ -942,7 +942,7 @@ def test_rebin_no_propagate(ndcube_2d_ln_lt_mask_uncert):
 
     cube._mask = False
     cube._uncertainty = UnknownUncertainty(cube.data * 0.1)
-    with pytest.warns(UserWarning, match="Uncertainty is an UnknownUncertainty which does not support uncertainty propagation."):
+    with pytest.warns(UserWarning, match="The uncertainty on this NDCube has no known way to propagate forward"):
         output = cube.rebin(bin_shape, operation=np.sum, propagate_uncertainties=True)
     assert output.uncertainty is None