diff --git a/firedrake/mg/ufl_utils.py b/firedrake/mg/ufl_utils.py
index c2e8ab69c9..bbc0086f11 100644
--- a/firedrake/mg/ufl_utils.py
+++ b/firedrake/mg/ufl_utils.py
@@ -180,9 +180,15 @@ def coarsen_function(expr, self, coefficient_mapping=None):
         coefficient_mapping = {}
     new = coefficient_mapping.get(expr)
     if new is None:
-        V = self(expr.function_space(), self)
-        new = firedrake.Function(V, name="coarse_%s" % expr.name())
+        Vf = expr.function_space()
+        Vc = self(Vf, self)
+        new = firedrake.Function(Vc, name="coarse_%s" % expr.name())
         expr._child = weakref.proxy(new)
+        manager = firedrake.dmhooks.get_transfer_manager(Vf.dm)
+        if isinstance(expr, firedrake.Cofunction):
+            manager.restrict(expr, new)
+        elif isinstance(expr, firedrake.Function):
+            manager.inject(expr, new)
     return new