diff --git a/newsfragments/320.misc.rst b/newsfragments/320.misc.rst
new file mode 100644
index 0000000000..3f799b9eb0
--- /dev/null
+++ b/newsfragments/320.misc.rst
@@ -0,0 +1,4 @@
+Entering a cancel scope whose deadline is in the past now immediately
+cancels it, so :exc:`~trio.Cancelled` will be raised by the first
+checkpoint in the cancel scope rather than the second one.
+This also affects constructs like ``with trio.move_on_after(0):``.
diff --git a/trio/_core/_run.py b/trio/_core/_run.py
index e00295a1ca..6faeced12f 100644
--- a/trio/_core/_run.py
+++ b/trio/_core/_run.py
@@ -201,6 +201,8 @@ def __enter__(self):
             )
         self._scope_task = task
         self.cancelled_caught = False
+        if current_time() >= self._deadline:
+            self.cancel_called = True
         with self._might_change_effective_deadline():
             self._add_task(task)
         return self
diff --git a/trio/_core/tests/test_run.py b/trio/_core/tests/test_run.py
index e03f6da03a..c6d3298bcd 100644
--- a/trio/_core/tests/test_run.py
+++ b/trio/_core/tests/test_run.py
@@ -407,12 +407,18 @@ async def main():
 
     _core.run(main, instruments=[r1, r2])
 
-    # It sleeps 5 times, so it runs 6 times
+    # It sleeps 5 times, so it runs 6 times.  Note that checkpoint()
+    # reschedules the task immediately upon yielding, before the
+    # after_task_step event fires.
     expected = (
-        [("before_run",)] +
-        6 * [("schedule", task),
+        [("before_run",),
+         ("schedule", task)] +
+        [("before", task),
+         ("schedule", task),
+         ("after", task)] * 5 + [
              ("before", task),
-             ("after", task)] + [("after_run",)]
+             ("after", task), ("after_run",)
+         ]
     )
     assert len(r1.record) > len(r2.record) > len(r3.record)
     assert r1.record == r2.record + r3.record
@@ -444,15 +450,15 @@ async def main():
         ("schedule", tasks["t2"]),
         {
             ("before", tasks["t1"]),
+            ("schedule", tasks["t1"]),
             ("after", tasks["t1"]),
             ("before", tasks["t2"]),
+            ("schedule", tasks["t2"]),
             ("after", tasks["t2"])
         },
         {
-            ("schedule", tasks["t1"]),
             ("before", tasks["t1"]),
             ("after", tasks["t1"]),
-            ("schedule", tasks["t2"]),
             ("before", tasks["t2"]),
             ("after", tasks["t2"])
         },
diff --git a/trio/_core/tests/tutil.py b/trio/_core/tests/tutil.py
index dc93794bef..d5d22d525e 100644
--- a/trio/_core/tests/tutil.py
+++ b/trio/_core/tests/tutil.py
@@ -52,7 +52,7 @@ def gc_collect_harder():
 
 
 # template is like:
-#   [1, {2.1, 2.2}, 3] -> matches [1, 2.1, 3] or [1, 2.2, 3]
+#   [1, {2.1, 2.2}, 3] -> matches [1, 2.1, 2.2, 3] or [1, 2.2, 2.1, 3]
 def check_sequence_matches(seq, template):
     i = 0
     for pattern in template: