diff --git a/devito/types/sparse.py b/devito/types/sparse.py
index f7f40fcaea..e05e5f7472 100644
--- a/devito/types/sparse.py
+++ b/devito/types/sparse.py
@@ -135,17 +135,21 @@ def __distributor_setup__(self, **kwargs):
     def __subfunc_setup__(self, suffix, keys, dtype=None, inkwargs=False, **kwargs):
         key = None
         for k in keys:
-            if k in kwargs:
-                if kwargs[k] is not None:
-                    key = kwargs[k]
-                    break
-                else:
-                    # In cases such as rebuild,
-                    # the subfunction may be passed explicitly as None
-                    return None
+            if k not in kwargs:
+                continue
+            elif kwargs[k] is None:
+                # In cases such as rebuild,
+                # the subfunction may be passed explicitly as None
+                return None
+            else:
+                key = kwargs[k]
+                break
         else:
             if inkwargs:
-                # Only create the subfunction if provided.
+                # Only create the subfunction if provided. This is useful
+                # with PrecomputedSparseFunctions that can have different subfunctions
+                # to skip creating extra if another one has already
+                # been provided
                 return None
 
         # Shape and dimensions from args
@@ -619,10 +623,14 @@ def _dist_subfunc_gather(self, sfuncd, subfunc):
         # `_dist_scatter` is here sent.
 
     def _dist_scatter(self, alias=None, data=None):
+        key = alias or self
         mapper = {self: self._dist_data_scatter(data=data)}
         for i in self._sub_functions:
-            if getattr(alias, i) is not None:
-                mapper.update(self._dist_subfunc_scatter(getattr(self, i)))
+            if getattr(key, i) is not None:
+                # Pick up alias' in case runtime SparseFunctions is missing
+                # a subfunction
+                sf = getattr(self, i) or getattr(key, i)
+                mapper.update(self._dist_subfunc_scatter(sf))
         return mapper
 
     def _eval_at(self, func):
@@ -662,7 +670,7 @@ def _arg_values(self, **kwargs):
             else:
                 # We've been provided a pure-data replacement (array)
                 values = {}
-                for k, v in self._dist_scatter(new).items():
+                for k, v in self._dist_scatter(data=new).items():
                     values[k.name] = v
                     for i, s in zip(k.indices, v.shape):
                         size = s - sum(k._size_nodomain[i])
@@ -859,7 +867,7 @@ def __init_finalize__(self, *args, **kwargs):
         super().__init_finalize__(*args, **kwargs)
 
         # Set up sparse point coordinates
-        keys = ('coordinates','coordinates_data')
+        keys = ('coordinates', 'coordinates_data')
         self._coordinates = self.__subfunc_setup__('coords', keys, **kwargs)
         self._dist_origin = {self._coordinates: self.grid.origin_offset}
 
@@ -1113,7 +1121,6 @@ def __init_finalize__(self, *args, **kwargs):
 
         if not any(k in kwargs for k in ('coordinates', 'gridpoints',
                                          'coordinates_data', 'gridpoints_data')):
-            print(kwargs)
             raise ValueError("PrecomputedSparseFunction requires `coordinates`"
                              "or `gridpoints` arguments")
 
diff --git a/tests/test_rebuild.py b/tests/test_rebuild.py
index 5498d819a7..79b2765a30 100644
--- a/tests/test_rebuild.py
+++ b/tests/test_rebuild.py
@@ -1,8 +1,8 @@
 import numpy as np
 import pytest
 
-from devito import Dimension, Function
-from devito.types import StencilDimension
+from devito import Dimension, Function, Grid
+from devito.types import StencilDimension, SparseFunction, PrecomputedSparseFunction
 from devito.data.allocators import DataReference
 
 
@@ -65,3 +65,19 @@ def test_stencil_dimension_borked(self):
 
         # TODO: Look into Symbol._cache_key and the way the key is generated
         assert sd0 is sd1
+
+
+class TestSparseFunction:
+
+    @pytest.mark.parametrize('sfunc', [SparseFunction, PrecomputedSparseFunction])
+    def test_none_subfunc(self, sfunc):
+        grid = Grid((4, 4))
+        coords = np.zeros((5, 2))
+
+        s = sfunc(name='s', grid=grid, npoint=5, coordinates=coords, r=1)
+
+        assert s.coordinates is not None
+
+        # Explicity set coordinates to None
+        sr = s._rebuild(function=None, initializer=None, coordinates=None)
+        assert sr.coordinates is None