diff --git a/firedrake/assemble.py b/firedrake/assemble.py
index f451b3f596..feb43f29bb 100644
--- a/firedrake/assemble.py
+++ b/firedrake/assemble.py
@@ -1180,25 +1180,24 @@ def allocate(self):
 
     def _apply_bc(self, tensor, bc):
         # TODO Maybe this could be a singledispatchmethod?
-        if isinstance(bc, DirichletBC):
-            self._apply_dirichlet_bc(tensor, bc)
-        elif isinstance(bc, EquationBCSplit):
-            bc.zero(tensor)
-            type(self)(bc.f, bcs=bc.bcs, form_compiler_parameters=self._form_compiler_params, needs_zeroing=False,
-                       zero_bc_nodes=self._zero_bc_nodes, diagonal=self._diagonal).assemble(tensor=tensor)
-        else:
-            raise AssertionError
-
-    def _apply_dirichlet_bc(self, tensor, bc):
-        if not self._zero_bc_nodes:
+        if self._diagonal:
+            assert isinstance(bc, DirichletBC)
+            assert not self._zero_bc_nodes
             tensor_func = tensor.riesz_representation(riesz_map="l2")
-            if self._diagonal:
-                bc.set(tensor_func, 1)
-            else:
-                bc.apply(tensor_func)
+            bc.set(tensor_func, 1)
             tensor.assign(tensor_func.riesz_representation(riesz_map="l2"))
         else:
-            bc.zero(tensor)
+            test, = self._form.arguments()
+            if test.function_space() == bc.function_space_parent:
+                if isinstance(bc, DirichletBC):
+                    assert self._zero_bc_nodes
+                    bc.zero(tensor)
+                elif isinstance(bc, EquationBCSplit):
+                    bc.zero(tensor)
+                    type(self)(bc.f, bcs=bc.bcs, form_compiler_parameters=self._form_compiler_params, needs_zeroing=False,
+                               zero_bc_nodes=self._zero_bc_nodes, diagonal=self._diagonal).assemble(tensor=tensor)
+                else:
+                    raise AssertionError
 
     def _check_tensor(self, tensor):
         if tensor.function_space() != self._form.arguments()[0].function_space():
@@ -1421,31 +1420,29 @@ def _apply_bc(self, tensor, bc):
         index = 0 if V.index is None else V.index
         space = V if V.parent is None else V.parent
         if isinstance(bc, DirichletBC):
-            if space != spaces[0]:
-                raise TypeError("bc space does not match the test function space")
-            elif space != spaces[1]:
-                raise TypeError("bc space does not match the trial function space")
-
-            # Set diagonal entries on bc nodes to 1 if the current
-            # block is on the matrix diagonal and its index matches the
-            # index of the function space the bc is defined on.
-            op2tensor[index, index].set_local_diagonal_entries(bc.nodes, idx=component, diag_val=self.weight)
-
+            if space == spaces[0] and space == spaces[1]:
+                # Set diagonal entries on bc nodes to 1 if the current
+                # block is on the matrix diagonal and its index matches the
+                # index of the function space the bc is defined on.
+                op2tensor[index, index].set_local_diagonal_entries(bc.nodes, idx=component, diag_val=self.weight)
             # Handle off-diagonal block involving real function space.
             # "lgmaps" is correctly constructed in _matrix_arg, but
             # is ignored by PyOP2 in this case.
             # Walk through row blocks associated with index.
-            for j, s in enumerate(space):
-                if j != index and s.ufl_element().family() == "Real":
-                    self._apply_bcs_mat_real_block(op2tensor, index, j, component, bc.node_set)
+            if space == spaces[0]:
+                for j, s in enumerate(spaces[1]):
+                    if j != index and s.ufl_element().family() == "Real":
+                        self._apply_bcs_mat_real_block(op2tensor, index, j, component, bc.node_set)
             # Walk through col blocks associated with index.
-            for i, s in enumerate(space):
-                if i != index and s.ufl_element().family() == "Real":
-                    self._apply_bcs_mat_real_block(op2tensor, i, index, component, bc.node_set)
+            if space == spaces[1]:
+                for i, s in enumerate(spaces[0]):
+                    if i != index and s.ufl_element().family() == "Real":
+                        self._apply_bcs_mat_real_block(op2tensor, i, index, component, bc.node_set)
         elif isinstance(bc, EquationBCSplit):
-            for j, s in enumerate(spaces[1]):
-                if s.ufl_element().family() == "Real":
-                    self._apply_bcs_mat_real_block(op2tensor, index, j, component, bc.node_set)
+            if space == spaces[0]:
+                for j, s in enumerate(spaces[1]):
+                    if s.ufl_element().family() == "Real":
+                        self._apply_bcs_mat_real_block(op2tensor, index, j, component, bc.node_set)
             type(self)(bc.f, bcs=bc.bcs, form_compiler_parameters=self._form_compiler_params, needs_zeroing=False).assemble(tensor=tensor)
         else:
             raise AssertionError
@@ -1889,19 +1886,13 @@ def get_indicess(self):
 
     def _filter_bcs(self, row, col):
         assert len(self._form.arguments()) == 2 and not self._diagonal
+        bcrow = [bc for bc in self._bcs if bc.function_space_parent == self.test_function_space]
+        bccol = [bc for bc in self._bcs if bc.function_space_parent == self.trial_function_space and isinstance(bc, DirichletBC)]
         if len(self.test_function_space) > 1:
-            bcrow = tuple(bc for bc in self._bcs
-                          if bc.function_space_index() == row)
-        else:
-            bcrow = self._bcs
-
+            bcrow = [bc for bc in bcrow if bc.function_space_index() == row]
         if len(self.trial_function_space) > 1:
-            bccol = tuple(bc for bc in self._bcs
-                          if bc.function_space_index() == col
-                          and isinstance(bc, DirichletBC))
-        else:
-            bccol = tuple(bc for bc in self._bcs if isinstance(bc, DirichletBC))
-        return bcrow, bccol
+            bccol = [bc for bc in bccol if bc.function_space_index() == col]
+        return tuple(bcrow), tuple(bccol)
 
     def needs_unrolling(self):
         """Do we need to address matrix elements directly rather than in
diff --git a/firedrake/bcs.py b/firedrake/bcs.py
index f0d007ede4..ae1f0b655c 100644
--- a/firedrake/bcs.py
+++ b/firedrake/bcs.py
@@ -63,6 +63,7 @@ def __init__(self, V, sub_domain):
             else:
                 # All done
                 break
+        self.function_space_parent = fs
         # Used for indexing functions passed in.
         self._indices = tuple(reversed(indices))
         # init bcs