diff --git a/course/models.py b/course/models.py
index f1f2fc873a3cf1a77da530174778b22abb5b2b5f..0a3dfe5462a54056e720172f8bdfe7ee0e6878e0 100644
--- a/course/models.py
+++ b/course/models.py
@@ -63,6 +63,7 @@ from course.page.base import AnswerFeedback
 if False:
     from typing import List, Dict, Any, Optional, Text, Iterable, Tuple, FrozenSet  # noqa
     from course.content import FlowDesc  # noqa
+    import datetime # noqa
 
 # }}}
 
@@ -819,6 +820,7 @@ class FlowSession(models.Model):
         return assemble_answer_visits(self)
 
     def last_activity(self):
+        # type: () -> Optional[datetime.datetime]
         for visit in (FlowPageVisit.objects
                 .filter(
                     flow_session=self,
diff --git a/course/utils.py b/course/utils.py
index 944fbcabbf8cc67e9e640836c522550b2d99f8e4..ffbee615d24e6df09fac72fbcd51266b399e3bad 100644
--- a/course/utils.py
+++ b/course/utils.py
@@ -493,9 +493,25 @@ def get_session_grading_rule(
 
         if hasattr(rule, "if_completed_before"):
             ds = parse_date_spec(session.course, rule.if_completed_before)
-            if session.in_progress and now_datetime > ds:
-                continue
-            if not session.in_progress and session.completion_time > ds:
+
+            use_last_activity_as_completion_time = False
+            if hasattr(rule, "use_last_activity_as_completion_time"):
+                use_last_activity_as_completion_time = \
+                        rule.use_last_activity_as_completion_time
+
+            if use_last_activity_as_completion_time:
+                last_activity = session.last_activity()
+                if last_activity is not None:
+                    completion_time = last_activity
+                else:
+                    completion_time = now_datetime
+            else:
+                if session.in_progress:
+                    completion_time = now_datetime
+                else:
+                    completion_time = session.completion_time
+
+            if completion_time > ds:
                 continue
 
         due = parse_date_spec(session.course, getattr(rule, "due", None))
diff --git a/doc/flow.rst b/doc/flow.rst
index b1cf6ba3c5544197976ca3c611467163a6cc0af3..a9886a90c51097a7c86e004e1372e061bcfaf55c 100644
--- a/doc/flow.rst
+++ b/doc/flow.rst
@@ -510,6 +510,12 @@ Determining how final (overall) grades of flows are computed
         (Optional) A :ref:`datespec <datespec>`. Rule applies if the session was completed before
         this time.
 
+        When evaluating this condition for in-progress sessions, the current time,
+        or, if :attr:`use_last_activity_as_completion_time` is set, the time of the
+        last activity is used.
+
+        Since September 2017, this respects :attr:`use_last_activity_as_completion_time`.
+
     .. rubric:: Rules specified
 
     .. attribute:: credit_percent