diff --git a/kopf/reactor/daemons.py b/kopf/reactor/daemons.py
index f083e6a..240330e 100644
--- a/kopf/reactor/daemons.py
+++ b/kopf/reactor/daemons.py
@@ -25,6 +25,8 @@ import time
 import warnings
 from typing import Collection, List, Mapping, MutableMapping, Sequence
 
+import aiojobs
+
 from kopf.engines import loggers
 from kopf.reactor import causation, effects, handling, lifecycles
 from kopf.storage import states
@@ -209,31 +211,71 @@ async def daemon_killer(
         *,
         settings: configuration.OperatorSettings,
         memories: containers.ResourceMemories,
+        freeze_checker: primitives.ToggleSet,
 ) -> None:
     """
-    An operator's root task to kill the daemons on the operator's shutdown.
-    """
+    An operator's root task to kill the daemons on the operator's demand.
+
+    The "demand" comes in two cases: when the operator is exiting (gracefully
+    or not), and when the operator is pausing because of peering. In that case,
+    all watch-streams are disconnected, and all daemons/timers should stop.
+
+    When pausing, the daemons/timers are stopped via their regular stopping
+    procedure: with graceful or forced termination, backoffs, timeouts.
+
+    .. warning::
+
+        Each daemon will be respawned on the next K8s watch-event strictly
+        after the previous daemon is fully stopped.
+        There are never 2 instances of the same daemon running in parallel.
 
-    # Sleep forever, or until cancelled, which happens when the operator begins its shutdown.
+        In normal cases (enough time is given to stop), this is usually done
+        by the post-freeze re-listing event. In rare cases when the unfreeze
+        happens faster than the daemon is stopped (highly unlikely to happen),
+        that event can be missed because the daemon is being stopped yet,
+        so the respawn can happen with a significant delay.
+
+        This issue is considered low-priority & auxiliary, so as the peering
+        itself. It can be fixed later. Workaround: make daemons to exit fast.
+    """
+    # Unlimited job pool size —- the same as if we would be managing the tasks directly.
+    # Unlimited timeout in `close()` -- since we have our own per-daemon timeout management.
+    scheduler: aiojobs.Scheduler = await aiojobs.create_scheduler(limit=None, close_timeout=99999)
     try:
-        await asyncio.Event().wait()
+        while True:
+
+            # Stay here while the operator is running normally, until it is frozen.
+            await freeze_checker.wait_for(True)
+
+            # The stopping tasks are "fire-and-forget" -- we do not get (or care of) the result.
+            # The daemons remain resumable, since they exit not on their own accord.
+            for memory in memories.iter_all_memories():
+                for daemon in memory.running_daemons.values():
+                    await scheduler.spawn(stop_daemon(
+                        settings=settings,
+                        daemon=daemon,
+                        reason=primitives.DaemonStoppingReason.OPERATOR_PAUSING))
+
+            # Stay here while the operator is frozen, until it is resumed.
+            # The fresh stream of watch-events will spawn new daemons naturally.
+            await freeze_checker.wait_for(False)
 
     # Terminate all running daemons when the operator exits (and this task is cancelled).
     finally:
-        tasks = [
-            aiotasks.create_task(
-                name=f"stop daemon {daemon.handler.id}",
-                coro=stop_daemon(daemon=daemon, settings=settings))
-            for memory in memories.iter_all_memories()
-            for daemon in memory.running_daemons.values()
-        ]
-        await aiotasks.wait(tasks)
+        for memory in memories.iter_all_memories():
+            for daemon in memory.running_daemons.values():
+                await scheduler.spawn(stop_daemon(
+                    settings=settings,
+                    daemon=daemon,
+                    reason=primitives.DaemonStoppingReason.OPERATOR_EXITING))
+        await scheduler.close()
 
 
 async def stop_daemon(
         *,
         settings: configuration.OperatorSettings,
         daemon: containers.Daemon,
+        reason: primitives.DaemonStoppingReason,
 ) -> None:
     """
     Stop a single daemon.
@@ -255,7 +297,7 @@ async def stop_daemon(
         raise RuntimeError(f"Unsupported daemon handler: {handler!r}")
 
     # Whatever happens with other flags & logs & timings, this flag must be surely set.
-    daemon.stopper.set(reason=primitives.DaemonStoppingReason.OPERATOR_EXITING)
+    daemon.stopper.set(reason=reason)
     await _wait_for_instant_exit(settings=settings, daemon=daemon)
 
     if daemon.task.done():
@@ -336,7 +378,7 @@ async def _runner(
     finally:
 
         # Prevent future re-spawns for those exited on their own, for no reason.
-        # Only the filter-mismatching daemons can be re-spawned on future events.
+        # Only the filter-mismatching or peering-frozen daemons can be re-spawned.
         if stopper.reason == primitives.DaemonStoppingReason.NONE:
             memory.forever_stopped.add(handler.id)
 
diff --git a/kopf/reactor/orchestration.py b/kopf/reactor/orchestration.py
index ec0b426..3271581 100644
--- a/kopf/reactor/orchestration.py
+++ b/kopf/reactor/orchestration.py
@@ -87,8 +87,8 @@ async def ochestrator(
         settings: configuration.OperatorSettings,
         identity: peering.Identity,
         insights: references.Insights,
+        freeze_checker: primitives.ToggleSet,
 ) -> None:
-    freeze_checker = primitives.ToggleSet()
     freeze_blocker = await freeze_checker.make_toggle(name='peering CRD is absent')
     ensemble = Ensemble(freeze_blocker=freeze_blocker, freeze_checker=freeze_checker)
     try:
diff --git a/kopf/reactor/running.py b/kopf/reactor/running.py
index e66ea48..3c0b33f 100644
--- a/kopf/reactor/running.py
+++ b/kopf/reactor/running.py
@@ -177,6 +177,7 @@ async def spawn_tasks(
     event_queue: posting.K8sEventQueue = asyncio.Queue()
     signal_flag: aiotasks.Future = asyncio.Future()
     started_flag: asyncio.Event = asyncio.Event()
+    freeze_checker = primitives.ToggleSet()
     tasks: MutableSequence[aiotasks.Task] = []
 
     # Map kwargs into the settings object.
@@ -223,7 +224,8 @@ async def spawn_tasks(
         name="daemon killer", flag=started_flag, logger=logger,
         coro=daemons.daemon_killer(
             settings=settings,
-            memories=memories)))
+            memories=memories,
+            freeze_checker=freeze_checker)))
 
     # Keeping the credentials fresh and valid via the authentication handlers on demand.
     tasks.append(aiotasks.create_guarded_task(
@@ -281,6 +283,7 @@ async def spawn_tasks(
                 settings=settings,
                 insights=insights,
                 identity=identity,
+                freeze_checker=freeze_checker,
                 processor=functools.partial(processing.process_resource_event,
                                             lifecycle=lifecycle,
                                             registry=registry,
diff --git a/kopf/structs/primitives.py b/kopf/structs/primitives.py
index 9980aba..d0d7476 100644
--- a/kopf/structs/primitives.py
+++ b/kopf/structs/primitives.py
@@ -230,6 +230,7 @@ class DaemonStoppingReason(enum.Flag):
     DONE = enum.auto()  # whatever the reason and the status, the asyncio task has exited.
     FILTERS_MISMATCH = enum.auto()  # the resource does not match the filters anymore.
     RESOURCE_DELETED = enum.auto()  # the resource was deleted, the asyncio task is still awaited.
+    OPERATOR_PAUSING = enum.auto()  # the operator is pausing, the asyncio task is still awaited.
     OPERATOR_EXITING = enum.auto()  # the operator is exiting, the asyncio task is still awaited.
     DAEMON_SIGNALLED = enum.auto()  # the stopper flag was set, the asyncio task is still awaited.
     DAEMON_CANCELLED = enum.auto()  # the asyncio task was cancelled, the thread can be running.

diff --git a/tests/handling/daemons/conftest.py b/tests/handling/daemons/conftest.py
index e2636ea..22b1812 100644
--- a/tests/handling/daemons/conftest.py
+++ b/tests/handling/daemons/conftest.py
@@ -6,10 +6,12 @@ import freezegun
 import pytest
 
 import kopf
+from kopf.reactor.daemons import daemon_killer
 from kopf.reactor.processing import process_resource_event
 from kopf.structs.bodies import RawBody
 from kopf.structs.containers import ResourceMemories
 from kopf.structs.memos import Memo
+from kopf.structs.primitives import ToggleSet
 
 
 class DaemonDummy:
@@ -76,6 +78,31 @@ def simulate_cycle(k8s_mocked, registry, settings, resource, memories, mocker):
     return _simulate_cycle
 
 
+@pytest.fixture()
+async def freeze_checker():
+    return ToggleSet()
+
+
+@pytest.fixture()
+async def freeze_toggle(freeze_checker: ToggleSet):
+    return await freeze_checker.make_toggle(name="freeze_toggle fixture")
+
+
+@pytest.fixture()
+async def background_daemon_killer(settings, memories, freeze_checker):
+    """
+    Run the daemon killer in the background.
+    """
+    task = asyncio.create_task(daemon_killer(
+        settings=settings, memories=memories, freeze_checker=freeze_checker))
+    yield
+    task.cancel()
+    try:
+        await task
+    except asyncio.CancelledError:
+        pass
+
+
 @pytest.fixture()
 def frozen_time():
     """
diff --git a/tests/handling/daemons/test_daemon_termination.py b/tests/handling/daemons/test_daemon_termination.py
index 2d89d22..3ec39de 100644
--- a/tests/handling/daemons/test_daemon_termination.py
+++ b/tests/handling/daemons/test_daemon_termination.py
@@ -18,7 +18,7 @@ async def test_daemon_exits_gracefully_and_instantly_via_stopper(
         dummy.steps['called'].set()
         await kwargs['stopped'].wait()
 
-    # 0th cycle:tTrigger spawning and wait until ready. Assume the finalizers are already added.
+    # 0th cycle: trigger spawning and wait until ready. Assume the finalizers are already added.
     finalizer = settings.persistence.finalizer
     event_object = {'metadata': {'finalizers': [finalizer]}}
     await simulate_cycle(event_object)
@@ -39,6 +39,41 @@ async def test_daemon_exits_gracefully_and_instantly_via_stopper(
     assert k8s_mocked.patch_obj.call_args_list[0][1]['patch']['metadata']['finalizers'] == []
 
 
+@pytest.mark.usefixtures('background_daemon_killer')
+async def test_daemon_exits_gracefully_and_instantly_via_peering_freeze(
+        settings, memories, resource, dummy, simulate_cycle, freeze_toggle,
+        caplog, assert_logs, k8s_mocked, frozen_time, mocker, timer):
+    caplog.set_level(logging.DEBUG)
+
+    # A daemon-under-test.
+    @kopf.daemon(*resource, id='fn')
+    async def fn(**kwargs):
+        dummy.kwargs = kwargs
+        dummy.steps['called'].set()
+        await kwargs['stopped'].wait()
+
+    # 0th cycle: trigger spawning and wait until ready. Assume the finalizers are already added.
+    finalizer = settings.persistence.finalizer
+    event_object = {'metadata': {'finalizers': [finalizer]}}
+    await simulate_cycle(event_object)
+    await dummy.steps['called'].wait()
+
+    # 1st stage: trigger termination due to peering freeze.
+    mocker.resetall()
+    await freeze_toggle.turn_to(True)
+
+    # Check that the daemon has exited near-instantly, with no delays.
+    with timer:
+        await dummy.wait_for_daemon_done()
+    assert timer.seconds < 0.01  # near-instantly
+
+    # There is no way to test for re-spawning here: it is done by watch-events,
+    # which are tested by the peering freezes elsewhere (test_daemon_spawning.py).
+    # We only test that it is capable for respawning (not forever-stopped):
+    memory = await memories.recall(event_object)
+    assert not memory.forever_stopped
+
+
 async def test_daemon_exits_instantly_via_cancellation_with_backoff(
         settings, resource, dummy, simulate_cycle,
         caplog, assert_logs, k8s_mocked, frozen_time, mocker):

timers continue when freezing operations
## Long story short

Thanks for creating kopf. I am currently developing an operator that updates Egress NetworkPolicy resources to sync its `spec.egress[*].to[*].ipBlock.cidr` keys with A records for DNS hostnames.

This operator used timers (looking into daemons to follow DNS TTL). I run an operator in k8s with cluster peering. For development I start a local instance with --dev.

I see the operator in k8s detects the development instance:

```
Freezing operations in favour of [<Peer rtoma@devsystem/20210208145159/nz5: priority=666, lifetime=60, lastseen='2021-02-08T14:52:01.160123'>].
```

The development instance's log show:

```
Resuming operations after the freeze. Conflicting operators with the same priority are gone.
```

Still both operator instances show `Timer 'NAME' succeeded` messages. I searched the docs, but could not find anything.

## Description

<!-- Please provide as much information as possible. Lack of information may result in a delayed response. As a guideline, use the following placeholders, and add yours as needed. -->

<details><summary>The code snippet to reproduce the issue</summary>

```python
import kopf
```
</details>

<details><summary>The exact command to reproduce the issue</summary>

```bash
kopf run ...
```
</details>

<details><summary>The full output of the command that failed</summary>

```
```
</details>


## Environment

<!-- The following commands can help:
     `kopf --version` or `pip show kopf`
     `kubectl version`
     `python --version`
-->

* Kopf version: 1.29.1
* Kubernetes version:  1.19.5
* Python version:  3.9.1
* OS/platform: k8s on pi4, local on arm mbp

<details><summary>Python packages installed</summary>
<!-- use `pip freeze --all` -->

```
```
</details>


tests/handling/daemons/test_daemon_termination.py::test_daemon_is_abandoned_due_to_cancellation_timeout_reached[namespaced]
tests/handling/daemons/test_daemon_termination.py::test_daemon_exits_gracefully_and_instantly_via_stopper[namespaced] tests/handling/daemons/test_daemon_termination.py::test_daemon_exits_gracefully_and_instantly_via_stopper[cluster] tests/handling/daemons/test_daemon_termination.py::test_daemon_exits_instantly_via_cancellation_with_backoff[namespaced] tests/handling/daemons/test_daemon_termination.py::test_daemon_exits_instantly_via_cancellation_with_backoff[cluster] tests/handling/daemons/test_daemon_termination.py::test_daemon_exits_slowly_via_cancellation_with_backoff[namespaced] tests/handling/daemons/test_daemon_termination.py::test_daemon_is_abandoned_due_to_cancellation_timeout_reached[cluster]