diff --git a/pyop2/codegen/builder.py b/pyop2/codegen/builder.py
index e8797888d..49183e112 100644
--- a/pyop2/codegen/builder.py
+++ b/pyop2/codegen/builder.py
@@ -22,7 +22,7 @@
 class PetscMat(OpaqueType):
 
     def __init__(self):
-        super(PetscMat, self).__init__(name="Mat")
+        super().__init__(name="Mat")
 
 
 class Map(object):
@@ -114,14 +114,17 @@ def pick_loop_indices(self, loop_index, layer_index=None, entity_index=None):
     def kernel_arg(self, loop_indices=None):
         pass
 
+    @abstractmethod
+    def emit_pack_instruction(self, *, loop_indices=None):
+        """Either yield an instruction, or else return an empty tuple (to indicate no instruction)"""
+
     @abstractmethod
     def pack(self, loop_indices=None):
         pass
 
     @abstractmethod
-    def emit_unpack_instruction(self, *,
-                                loop_indices=None):
-        pass
+    def emit_unpack_instruction(self, *, loop_indices=None):
+        """Either yield an instruction, or else return an empty tuple (to indicate no instruction)"""
 
 
 class GlobalPack(Pack):
@@ -133,12 +136,20 @@ def __init__(self, outer, access):
     def kernel_arg(self, loop_indices=None):
         return Indexed(self.outer, (Index(e) for e in self.outer.shape))
 
+    def emit_pack_instruction(self, *, loop_indices=None):
+        shape = self.outer.shape
+        if self.access is WRITE:
+            zero = Zero((), self.outer.dtype)
+            multiindex = MultiIndex(*(Index(e) for e in shape))
+            yield Accumulate(PackInst(), Indexed(self.outer, multiindex), zero)
+        else:
+            return ()
+
     def pack(self, loop_indices=None):
         return None
 
-    def emit_unpack_instruction(self, *,
-                                loop_indices=None):
-        yield None
+    def emit_unpack_instruction(self, *, loop_indices=None):
+        return ()
 
 
 class DatPack(Pack):
@@ -215,13 +226,15 @@ def kernel_arg(self, loop_indices=None):
             shape = pack.shape
             return Indexed(pack, (Index(e) for e in shape))
 
-    def emit_unpack_instruction(self, *,
-                                loop_indices=None):
+    def emit_pack_instruction(self, *, loop_indices=None):
+        return ()
+
+    def emit_unpack_instruction(self, *, loop_indices=None):
         pack = self.pack(loop_indices)
         if pack is None:
-            yield None
+            return ()
         elif self.access is READ:
-            yield None
+            return ()
         elif self.access in {INC, MIN, MAX}:
             op = {INC: Sum,
                   MIN: Min,
@@ -295,10 +308,13 @@ def kernel_arg(self, loop_indices=None):
         shape = pack.shape
         return Indexed(pack, (Index(e) for e in shape))
 
+    def emit_pack_instruction(self, *, loop_indices=None):
+        return ()
+
     def emit_unpack_instruction(self, *, loop_indices=None):
         pack = self.pack(loop_indices)
         if self.access is READ:
-            yield None
+            return ()
         else:
             if self.interior_horizontal:
                 _shape = (2,)
@@ -368,8 +384,10 @@ def kernel_arg(self, loop_indices=None):
         pack = self.pack(loop_indices=loop_indices)
         return Indexed(pack, tuple(Index(e) for e in pack.shape))
 
-    def emit_unpack_instruction(self, *,
-                                loop_indices=None):
+    def emit_pack_instruction(self, *, loop_indices=None):
+        return ()
+
+    def emit_unpack_instruction(self, *, loop_indices=None):
         from pyop2.codegen.rep2loopy import register_petsc_function
         ((rdim, cdim), ), = self.dims
         rmap, cmap = self.maps
@@ -428,7 +446,6 @@ class WrapperBuilder(object):
 
     def __init__(self, *, iterset, iteration_region=None, single_cell=False,
                  pass_layer_to_kernel=False, forward_arg_types=()):
-        super().__init__()
         self.arguments = []
         self.argument_accesses = []
         self.packed_args = []
@@ -658,14 +675,13 @@ def kernel_call(self):
         return FunctionCall(self.kernel.name, KernelInst(), access, free_indices, *args)
 
     def emit_instructions(self):
+        yield from itertools.chain(*(pack.emit_pack_instruction(loop_indices=self.loop_indices)
+                                     for pack in self.packed_args))
         # Sometimes, actual instructions do not refer to all the loop
         # indices (e.g. all of them are globals). To ensure that loopy
         # knows about these indices, we emit a dummy instruction (that
         # doesn't generate any code) that does depend on them.
         yield DummyInstruction(PackInst(), *(x for x in self.loop_indices if x is not None))
         yield self.kernel_call()
-        for pack in self.packed_args:
-            insns = pack.emit_unpack_instruction(loop_indices=self.loop_indices)
-            for insn in insns:
-                if insn is not None:
-                    yield insn
+        yield from itertools.chain(*(pack.emit_unpack_instruction(loop_indices=self.loop_indices)
+                                     for pack in self.packed_args))