@@ -15,6 +15,10 @@
 from __future__ import absolute_import, division
 
 
+MIN_ACK_DEADLINE = 10
+MAX_ACK_DEADLINE = 600
+
+
 class Histogram(object):
     """Representation of a single histogram.
 
@@ -27,8 +31,9 @@ class Histogram(object):
     are free to use a different formula.
 
     The precision of data stored is to the nearest integer. Additionally,
-    values outside the range of ``10 <= x <= 600`` are stored as ``10`` or
-    ``600``, since these are the boundaries of leases in the actual API.
+    values outside the range of ``MIN_ACK_DEADLINE <= x <= MAX_ACK_DEADLINE`` are stored
+    as ``MIN_ACK_DEADLINE`` or ``MAX_ACK_DEADLINE``, since these are the boundaries of
+    leases in the actual API.
     """
 
     def __init__(self, data=None):
@@ -83,41 +88,43 @@ def __repr__(self):
     def max(self):
         """Return the maximum value in this histogram.
 
-        If there are no values in the histogram at all, return 600.
+        If there are no values in the histogram at all, return ``MAX_ACK_DEADLINE``.
 
         Returns:
             int: The maximum value in the histogram.
         """
         if len(self._data) == 0:
-            return 600
+            return MAX_ACK_DEADLINE
         return next(iter(reversed(sorted(self._data.keys()))))
 
     @property
     def min(self):
         """Return the minimum value in this histogram.
 
-        If there are no values in the histogram at all, return 10.
+        If there are no values in the histogram at all, return ``MIN_ACK_DEADLINE``.
 
         Returns:
             int: The minimum value in the histogram.
         """
         if len(self._data) == 0:
-            return 10
+            return MIN_ACK_DEADLINE
         return next(iter(sorted(self._data.keys())))
 
     def add(self, value):
         """Add the value to this histogram.
 
         Args:
-            value (int): The value. Values outside of ``10 <= x <= 600``
-                will be raised to ``10`` or reduced to ``600``.
+            value (int): The value. Values outside of
+            ``MIN_ACK_DEADLINE <= x <= MAX_ACK_DEADLINE``
+                will be raised to ``MIN_ACK_DEADLINE`` or reduced to
+                ``MAX_ACK_DEADLINE``.
         """
         # If the value is out of bounds, bring it in bounds.
         value = int(value)
-        if value < 10:
-            value = 10
-        if value > 600:
-            value = 600
+        if value < MIN_ACK_DEADLINE:
+            value = MIN_ACK_DEADLINE
+        elif value > MAX_ACK_DEADLINE:
+            value = MAX_ACK_DEADLINE
 
         # Add the value to the histogram's data dictionary.
         self._data.setdefault(value, 0)
@@ -129,7 +136,7 @@ def percentile(self, percent):
 
         Args:
             percent (Union[int, float]): The precentile being sought. The
-                default consumer implementations use consistently use ``99``.
+                default consumer implementations consistently use ``99``.
 
         Returns:
             int: The value corresponding to the requested percentile.
@@ -150,5 +157,5 @@ def percentile(self, percent):
                 return k
 
         # The only way to get here is if there was no data.
-        # In this case, just return 10 seconds.
-        return 10
+        # In this case, just return the shortest possible deadline.
+        return MIN_ACK_DEADLINE
@@ -128,7 +128,9 @@ def maintain_leases(self):
             # Determine the appropriate duration for the lease. This is
             # based off of how long previous messages have taken to ack, with
             # a sensible default and within the ranges allowed by Pub/Sub.
-            deadline = self._manager.ack_deadline
+            # Also update the deadline currently used if enough new ACK data has been
+            # gathered since the last deadline update.
+            deadline = self._manager._obtain_ack_deadline(maybe_update=True)
             _LOGGER.debug("The current deadline value is %d seconds.", deadline)
 
             # Make a copy of the leased messages. This is needed because it's
 
@@ -143,7 +143,7 @@ def __init__(
         self._await_callbacks_on_shutdown = await_callbacks_on_shutdown
         self._ack_histogram = histogram.Histogram()
         self._last_histogram_size = 0
-        self._ack_deadline = 10
+        self._ack_deadline = histogram.MIN_ACK_DEADLINE
         self._rpc = None
         self._callback = None
         self._closing = threading.Lock()
@@ -179,6 +179,11 @@ def __init__(
         # currently on hold.
         self._pause_resume_lock = threading.Lock()
 
+        # A lock protecting the current ACK deadline used in the lease management. This
+        # value can be potentially updated both by the leaser thread and by the message
+        # consumer thread when invoking the internal _on_response() callback.
+        self._ack_deadline_lock = threading.Lock()
+
         # The threads created in ``.open()``.
         self._dispatcher = None
         self._leaser = None
@@ -223,29 +228,49 @@ def ack_histogram(self):
 
     @property
     def ack_deadline(self):
-        """Return the current ack deadline based on historical time-to-ack.
-
-        This method is "sticky". It will only perform the computations to
-        check on the right ack deadline if the histogram has gained a
-        significant amount of new information.
+        """Return the current ACK deadline based on historical data without updating it.
 
         Returns:
             int: The ack deadline.
         """
-        target_size = min(
-            self._last_histogram_size * 2, self._last_histogram_size + 100
-        )
-        hist_size = len(self.ack_histogram)
+        return self._obtain_ack_deadline(maybe_update=False)
+
+    def _obtain_ack_deadline(self, maybe_update: bool) -> int:
+        """The actual `ack_deadline` implementation.
+
+        This method is "sticky". It will only perform the computations to check on the
+        right ACK deadline if explicitly requested AND if the histogram with past
+        time-to-ack data has gained a significant amount of new information.
+
+        Args:
+            maybe_update (bool):
+                If ``True``, also update the current ACK deadline before returning it if
+                enough new ACK data has been gathered.
 
-        if hist_size > target_size:
-            self._last_histogram_size = hist_size
-            self._ack_deadline = self.ack_histogram.percentile(percent=99)
+        Returns:
+            int: The current ACK deadline in seconds to use.
+        """
+        with self._ack_deadline_lock:
+            if not maybe_update:
+                return self._ack_deadline
 
-        if self.flow_control.max_duration_per_lease_extension > 0:
-            self._ack_deadline = min(
-                self._ack_deadline, self.flow_control.max_duration_per_lease_extension
+            target_size = min(
+                self._last_histogram_size * 2, self._last_histogram_size + 100
             )
-        return self._ack_deadline
+            hist_size = len(self.ack_histogram)
+
+            if hist_size > target_size:
+                self._last_histogram_size = hist_size
+                self._ack_deadline = self.ack_histogram.percentile(percent=99)
+
+            if self.flow_control.max_duration_per_lease_extension > 0:
+                # The setting in flow control could be too low, adjust if needed.
+                flow_control_setting = max(
+                    self.flow_control.max_duration_per_lease_extension,
+                    histogram.MIN_ACK_DEADLINE,
+                )
+                self._ack_deadline = min(self._ack_deadline, flow_control_setting)
+            return self._ack_deadline
 
     @property
     def load(self):
@@ -490,7 +515,7 @@ def open(self, callback, on_callback_error):
         )
 
         # Create the RPC
-        stream_ack_deadline_seconds = self.ack_histogram.percentile(99)
+        stream_ack_deadline_seconds = self.ack_deadline
 
         get_initial_request = functools.partial(
             self._get_initial_request, stream_ack_deadline_seconds
@@ -688,7 +713,7 @@ def _on_response(self, response):
         # modack the messages we received, as this tells the server that we've
         # received them.
         items = [
-            requests.ModAckRequest(message.ack_id, self._ack_histogram.percentile(99))
+            requests.ModAckRequest(message.ack_id, self.ack_deadline)
             for message in received_messages
         ]
         self._dispatcher.modify_ack_deadline(items)
 
@@ -152,7 +152,8 @@ class LimitExceededBehavior(str, enum.Enum):
 FlowControl.max_duration_per_lease_extension.__doc__ = (
     "The max amount of time in seconds for a single lease extension attempt. "
     "Bounds the delay before a message redelivery if the subscriber "
-    "fails to extend the deadline."
+    "fails to extend the deadline. Must be between 10 and 600 (inclusive). Ignored "
+    "if set to 0."
 )
 
 
 
@@ -33,7 +33,7 @@ def test_contains():
 
 def test_max():
     histo = histogram.Histogram()
-    assert histo.max == 600
+    assert histo.max == histogram.MAX_ACK_DEADLINE
     histo.add(120)
     assert histo.max == 120
     histo.add(150)
@@ -44,7 +44,7 @@ def test_max():
 
 def test_min():
     histo = histogram.Histogram()
-    assert histo.min == 10
+    assert histo.min == histogram.MIN_ACK_DEADLINE
     histo.add(60)
     assert histo.min == 60
     histo.add(30)
@@ -63,20 +63,23 @@ def test_add():
 
 def test_add_lower_limit():
     histo = histogram.Histogram()
-    histo.add(5)
-    assert 5 not in histo
-    assert 10 in histo
+    low_value = histogram.MIN_ACK_DEADLINE - 1
+    histo.add(low_value)
+    assert low_value not in histo
+    assert histogram.MIN_ACK_DEADLINE in histo
 
 
 def test_add_upper_limit():
     histo = histogram.Histogram()
-    histo.add(12000)
-    assert 12000 not in histo
-    assert 600 in histo
+    high_value = histogram.MAX_ACK_DEADLINE + 1
+    histo.add(high_value)
+    assert high_value not in histo
+    assert histogram.MAX_ACK_DEADLINE in histo
 
 
 def test_percentile():
     histo = histogram.Histogram()
+    assert histo.percentile(42) == histogram.MIN_ACK_DEADLINE  # default when empty
     [histo.add(i) for i in range(101, 201)]
     assert histo.percentile(100) == 200
     assert histo.percentile(101) == 200
 
@@ -84,7 +84,7 @@ def create_manager(flow_control=types.FlowControl()):
     manager.is_active = True
     manager.flow_control = flow_control
     manager.ack_histogram = histogram.Histogram()
-    manager.ack_deadline = 10
+    manager._obtain_ack_deadline.return_value = 10
     return manager
Original file line number	Diff line number	Diff line change
`@@ -152,7 +152,8 @@ class LimitExceededBehavior(str, enum.Enum):`
`152`	`152`	`FlowControl.max_duration_per_lease_extension.__doc__ = (`
`153`	`153`	`"The max amount of time in seconds for a single lease extension attempt. "`
`154`	`154`	`"Bounds the delay before a message redelivery if the subscriber "`
`155`		`- "fails to extend the deadline."`
	`155`	`+ "fails to extend the deadline. Must be between 10 and 600 (inclusive). Ignored "`
	`156`	`+ "if set to 0."`
`156`	`157`	`)`
`157`	`158`
`158`	`159`