diff --git a/docs/source/news.rst b/docs/source/news.rst
index a33af13..501d6cf 100644
--- a/docs/source/news.rst
+++ b/docs/source/news.rst
@@ -9,6 +9,10 @@ Features:
 * ``Action.continue_task`` now takes ``action_task`` and extra fields to use for the action, so the default ``eliot:remote_task`` can be changed.
 * Added support for Python 3.10.
 
+Bug fixes:
+
+* Fix infinite recursion when a logging destination raises exceptions forever. Thanks to to @alextatarinov.
+
 1.13.0
 ^^^^^^
 
diff --git a/eliot/_action.py b/eliot/_action.py
index 56d9b4f..7ecbd11 100644
--- a/eliot/_action.py
+++ b/eliot/_action.py
@@ -440,7 +440,9 @@ class Action(object):
         fields[TASK_UUID_FIELD] = self._identification[TASK_UUID_FIELD]
         fields[TASK_LEVEL_FIELD] = self._nextTaskLevel().as_list()
         fields[MESSAGE_TYPE_FIELD] = message_type
-        self._logger.write(fields, fields.pop("__eliot_serializer__", None))
+        # Loggers will hopefully go away...
+        logger = fields.pop("__eliot_logger__", self._logger)
+        logger.write(fields, fields.pop("__eliot_serializer__", None))
 
 
 class WrongTask(Exception):
@@ -951,10 +953,10 @@ def log_message(message_type, **fields):
 
     If there is no current action, a new UUID will be generated.
     """
-    # Loggers will hopefully go away...
-    logger = fields.pop("__eliot_logger__", None)
     action = current_action()
     if action is None:
+        # Loggers will hopefully go away...
+        logger = fields.pop("__eliot_logger__", None)
         action = Action(logger, str(uuid4()), TaskLevel(level=[]), "")
     action.log(message_type, **fields)
 
diff --git a/eliot/_message.py b/eliot/_message.py
index d8eaef6..ca4aa52 100644
--- a/eliot/_message.py
+++ b/eliot/_message.py
@@ -116,10 +116,10 @@ class Message(object):
         Byte field names will be converted to Unicode.
 
         @type logger: L{eliot.ILogger} or C{None} indicating the default one.
+            Should not be set if the action is also set.
 
-        @param action: The L{Action} which is the context for this message. If
-            C{None}, the L{Action} will be deduced from the current call
-            stack.
+        @param action: The L{Action} which is the context for this message.  If
+            C{None}, the L{Action} will be deduced from the current call stack.
         """
         fields = dict(self._contents)
         if "message_type" not in fields:
@@ -127,7 +127,8 @@ class Message(object):
         if self._serializer is not None:
             fields["__eliot_serializer__"] = self._serializer
         if action is None:
-            fields["__eliot_logger__"] = logger
+            if logger is not None:
+                fields["__eliot_logger__"] = logger
             log_message(**fields)
         else:
             action.log(**fields)
diff --git a/eliot/_output.py b/eliot/_output.py
index debff7c..9d22e1d 100644
--- a/eliot/_output.py
+++ b/eliot/_output.py
@@ -2,7 +2,6 @@
 Implementation of hooks and APIs for outputting log messages.
 """
 
-import sys
 import traceback
 import inspect
 import json as pyjson
@@ -22,16 +21,9 @@ from .json import EliotJSONEncoder
 from ._validation import ValidationError
 
 
-class _DestinationsSendError(Exception):
-    """
-    An error occured sending to one or more destinations.
-
-    @ivar errors: A list of tuples output from C{sys.exc_info()}.
-    """
-
-    def __init__(self, errors):
-        self.errors = errors
-        Exception.__init__(self, errors)
+# Action type for log messages due to a (hopefully temporarily) broken
+# destination.
+DESTINATION_FAILURE = "eliot:destination_failure"
 
 
 class BufferingDestination(object):
@@ -70,24 +62,57 @@ class Destinations(object):
         """
         self._globalFields.update(fields)
 
-    def send(self, message):
+    def send(self, message, logger=None):
         """
         Deliver a message to all destinations.
 
         The passed in message might be mutated.
 
+        This should never raise an exception.
+
         @param message: A message dictionary that can be serialized to JSON.
         @type message: L{dict}
+
+        @param logger: The ``ILogger`` that wrote the message, if any.
         """
         message.update(self._globalFields)
         errors = []
+        is_destination_error_message = (
+            message.get("message_type", None) == DESTINATION_FAILURE
+        )
         for dest in self._destinations:
             try:
                 dest(message)
+            except Exception as e:
+                # If the destination is broken not because of a specific
+                # message, but rather continously, we will get a
+                # "eliot:destination_failure" log message logged, and so we
+                # want to ensure it doesn't do infinite recursion.
+                if not is_destination_error_message:
+                    errors.append(e)
+
+        for exception in errors:
+            from ._action import log_message
+
+            try:
+                new_msg = {
+                    MESSAGE_TYPE_FIELD: DESTINATION_FAILURE,
+                    REASON_FIELD: safeunicode(exception),
+                    EXCEPTION_FIELD: exception.__class__.__module__
+                    + "."
+                    + exception.__class__.__name__,
+                    "message": _safe_unicode_dictionary(message),
+                }
+                if logger is not None:
+                    # This is really only useful for testing, should really
+                    # figure out way to get rid of this mechanism...
+                    new_msg["__eliot_logger__"] = logger
+                log_message(**new_msg)
             except:
-                errors.append(sys.exc_info())
-        if errors:
-            raise _DestinationsSendError(errors)
+                # Nothing we can do here, raising exception to caller will
+                # break business logic, better to have that continue to
+                # work even if logging isn't.
+                pass
 
     def add(self, *destinations):
         """
@@ -144,6 +169,28 @@ class ILogger(Interface):
         """
 
 
+def _safe_unicode_dictionary(dictionary):
+    """
+    Serialize a dictionary to a unicode string no matter what it contains.
+
+    The resulting dictionary will loosely follow Python syntax but it is
+    not expected to actually be a lossless encoding in all cases.
+
+    @param dictionary: A L{dict} to serialize.
+
+    @return: A L{unicode} string representing the input dictionary as
+        faithfully as can be done without putting in too much effort.
+    """
+    try:
+        return str(
+            dict(
+                (saferepr(key), saferepr(value)) for (key, value) in dictionary.items()
+            )
+        )
+    except:
+        return saferepr(dictionary)
+
+
 @implementer(ILogger)
 class Logger(object):
     """
@@ -155,29 +202,6 @@ class Logger(object):
     """
 
     _destinations = Destinations()
-    _log_tracebacks = True
-
-    def _safeUnicodeDictionary(self, dictionary):
-        """
-        Serialize a dictionary to a unicode string no matter what it contains.
-
-        The resulting dictionary will loosely follow Python syntax but it is
-        not expected to actually be a lossless encoding in all cases.
-
-        @param dictionary: A L{dict} to serialize.
-
-        @return: A L{unicode} string representing the input dictionary as
-            faithfully as can be done without putting in too much effort.
-        """
-        try:
-            return str(
-                dict(
-                    (saferepr(key), saferepr(value))
-                    for (key, value) in dictionary.items()
-                )
-            )
-        except:
-            return saferepr(dictionary)
 
     def write(self, dictionary, serializer=None):
         """
@@ -193,38 +217,12 @@ class Logger(object):
 
             log_message(
                 "eliot:serialization_failure",
-                message=self._safeUnicodeDictionary(dictionary),
+                message=_safe_unicode_dictionary(dictionary),
                 __eliot_logger__=self,
             )
             return
 
-        try:
-            self._destinations.send(dictionary)
-        except _DestinationsSendError as e:
-            from ._action import log_message
-
-            if self._log_tracebacks:
-                for (exc_type, exception, exc_traceback) in e.errors:
-                    # Can't use same Logger as serialization errors because
-                    # if destination continues to error out we will get
-                    # infinite recursion. So instead we have to manually
-                    # construct a Logger that won't retry.
-                    logger = Logger()
-                    logger._log_tracebacks = False
-                    logger._destinations = self._destinations
-                    msg = {
-                        MESSAGE_TYPE_FIELD: "eliot:destination_failure",
-                        REASON_FIELD: safeunicode(exception),
-                        EXCEPTION_FIELD: exc_type.__module__ + "." + exc_type.__name__,
-                        "message": self._safeUnicodeDictionary(dictionary),
-                        "__eliot_logger__": logger,
-                    }
-                    log_message(**msg)
-            else:
-                # Nothing we can do here, raising exception to caller will
-                # break business logic, better to have that continue to
-                # work even if logging isn't.
-                pass
+        self._destinations.send(dictionary, self)
 
 
 def exclusively(f):
diff --git a/setup.cfg b/setup.cfg
index 259cc72..2268133 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -16,3 +16,6 @@ versionfile_build = eliot/_version.py
 tag_prefix = 
 parentdir_prefix = eliot-
 
+[flake8]
+max-line-length = 88
+extend-ignore = E203
\ No newline at end of file

diff --git a/eliot/tests/test_output.py b/eliot/tests/test_output.py
index 6b608c6..078f3e1 100644
--- a/eliot/tests/test_output.py
+++ b/eliot/tests/test_output.py
@@ -27,8 +27,9 @@ from .._output import (
     bytesjson as json,
     to_file,
     FileDestination,
-    _DestinationsSendError,
+    _safe_unicode_dictionary,
 )
+from .._action import start_action
 from .._validation import ValidationError, Field, _MessageSerializer
 from .._traceback import write_traceback
 from ..testing import assertContainsFields
@@ -372,7 +373,7 @@ class DestinationsTests(TestCase):
         self.assertEqual(dest2, [message])
         self.assertEqual(dest3, [message])
 
-    def test_destinationExceptionMultipleDestinations(self):
+    def test_destination_exception_multiple_destinations(self):
         """
         If one destination throws an exception, other destinations still
         get the message.
@@ -386,10 +387,11 @@ class DestinationsTests(TestCase):
         destinations.add(dest3.append)
 
         message = {"hello": 123}
-        self.assertRaises(_DestinationsSendError, destinations.send, {"hello": 123})
-        self.assertEqual((dest, dest3), ([message], [message]))
+        destinations.send(message)
+        self.assertIn(message, dest)
+        self.assertIn(message, dest3)
 
-    def test_destinationExceptionContinue(self):
+    def test_destination_exception_continue(self):
         """
         If a destination throws an exception, future messages are still
         sent to it.
@@ -398,9 +400,12 @@ class DestinationsTests(TestCase):
         dest = BadDestination()
         destinations.add(dest)
 
-        self.assertRaises(_DestinationsSendError, destinations.send, {"hello": 123})
-        destinations.send({"hello": 200})
-        self.assertEqual(dest, [{"hello": 200}])
+        msg1 = {"hello": 123}
+        msg2 = {"world": 456}
+        destinations.send(msg1)
+        self.assertNotIn(msg1, dest)
+        destinations.send(msg2)
+        self.assertIn(msg2, dest)
 
     def test_remove(self):
         """
@@ -560,9 +565,9 @@ class LoggerTests(TestCase):
         logger.write(d, serializer)
         self.assertEqual(d, original)
 
-    def test_safeUnicodeDictionary(self):
+    def test_safe_unicode_dictionary(self):
         """
-        L{Logger._safeUnicodeDictionary} converts the given dictionary's
+        L{_safe_unicode_dictionary} converts the given dictionary's
         values and keys to unicode using C{safeunicode}.
         """
 
@@ -573,20 +578,20 @@ class LoggerTests(TestCase):
         dictionary = {badobject(): 123, 123: badobject()}
         badMessage = "eliot: unknown, unicode() raised exception"
         self.assertEqual(
-            eval(Logger()._safeUnicodeDictionary(dictionary)),
+            eval(_safe_unicode_dictionary(dictionary)),
             {badMessage: "123", "123": badMessage},
         )
 
-    def test_safeUnicodeDictionaryFallback(self):
+    def test_safe_unicode_dictionary_fallback(self):
         """
         If converting the dictionary failed for some reason,
-        L{Logger._safeUnicodeDictionary} runs C{repr} on the object.
+        L{_safe_unicode_dictionary} runs C{repr} on the object.
         """
-        self.assertEqual(Logger()._safeUnicodeDictionary(None), "None")
+        self.assertEqual(_safe_unicode_dictionary(None), "None")
 
-    def test_safeUnicodeDictionaryFallbackFailure(self):
+    def test_safe_unicode_dictionary_fallback_failure(self):
         """
-        If all else fails, L{Logger._safeUnicodeDictionary} just gives up.
+        If all else fails, L{_safe_unicode_dictionary} just gives up.
         """
 
         class badobject(object):
@@ -594,7 +599,7 @@ class LoggerTests(TestCase):
                 raise TypeError()
 
         self.assertEqual(
-            Logger()._safeUnicodeDictionary(badobject()),
+            _safe_unicode_dictionary(badobject()),
             "eliot: unknown, unicode() raised exception",
         )
 
@@ -628,7 +633,7 @@ class LoggerTests(TestCase):
             },
         )
         self.assertIn("RuntimeError: oops", tracebackMessage["traceback"])
-        # Calling _safeUnicodeDictionary multiple times leads to
+        # Calling _safe_unicode_dictionary multiple times leads to
         # inconsistent results due to hash ordering, so compare contents:
         assertContainsFields(
             self, written[1], {"message_type": "eliot:serialization_failure"}
@@ -638,7 +643,7 @@ class LoggerTests(TestCase):
             dict((repr(key), repr(value)) for (key, value) in message.items()),
         )
 
-    def test_destinationExceptionCaught(self):
+    def test_destination_exception_caught(self):
         """
         If a destination throws an exception, an appropriate error is
         logged.
@@ -655,13 +660,13 @@ class LoggerTests(TestCase):
             dest[0],
             {
                 "message_type": "eliot:destination_failure",
-                "message": logger._safeUnicodeDictionary(message),
+                "message": _safe_unicode_dictionary(message),
                 "reason": "ono",
                 "exception": "eliot.tests.test_output.MyException",
             },
         )
 
-    def test_destinationMultipleExceptionsCaught(self):
+    def test_destination_multiple_exceptions_caught(self):
         """
         If multiple destinations throw an exception, an appropriate error is
         logged for each.
@@ -705,13 +710,13 @@ class LoggerTests(TestCase):
                     message,
                     {
                         "message_type": "eliot:destination_failure",
-                        "message": logger._safeUnicodeDictionary(message),
+                        "message": _safe_unicode_dictionary(message),
                         "reason": "ono",
                         "exception": "eliot.tests.test_output.MyException",
                     },
                     {
                         "message_type": "eliot:destination_failure",
-                        "message": logger._safeUnicodeDictionary(message),
+                        "message": _safe_unicode_dictionary(message),
                         "reason": zero_divide,
                         "exception": zero_type,
                     },
@@ -719,7 +724,7 @@ class LoggerTests(TestCase):
             ),
         )
 
-    def test_destinationExceptionCaughtTwice(self):
+    def test_destination_exception_caught_twice(self):
         """
         If a destination throws an exception, and the logged error about
         it also causes an exception, then just drop that exception on the
@@ -733,10 +738,15 @@ class LoggerTests(TestCase):
 
         logger._destinations.add(always_raise)
 
-        # No exception raised; since everything is dropped no other
-        # assertions to be made.
+        # Just a message. No exception raised; since everything is dropped no
+        # other assertions to be made.
         logger.write({"hello": 123})
 
+        # With an action. No exception raised; since everything is dropped no
+        # other assertions to be made.
+        with start_action(logger, "sys:do"):
+            logger.write({"hello": 123})
+
 
 class PEP8Tests(TestCase):
     """

In case of _DestinationsSendError inside a start_action block, infinite recursion occurs
If the Destination is broken regardless of the message, meaning it cannot log the "eliot:destination_failure" message, for instance (this is obviously, a simplification):

    class BrokenDestination():
        def __call__(self, message):
            raise ValueError

And there is current action, the `log_message` will not use a "Logger that won't retry", contrary to the comment in the code, but the action's one that **does** retry, leading to infinite recursion.

Now, I am not actually sure what's the fix should be but will be happy to submit a pull request if the solution is proposed. One idea that comes to mind is to override `action._logger` if the `current_action()` is not None. 

https://github.com/itamarst/eliot/blob/8609d380866491abe9e97eb814e4a04478b5893e/eliot/_output.py#L208-L222
https://github.com/itamarst/eliot/blob/8609d380866491abe9e97eb814e4a04478b5893e/eliot/_action.py#L932-L942
eliot/tests/test_output.py::MemoryLoggerTests::test_JSON eliot/tests/test_output.py::MemoryLoggerTests::test_JSON_custom_encoder eliot/tests/test_output.py::MemoryLoggerTests::test_bytesMustBeUTF8 eliot/tests/test_output.py::MemoryLoggerTests::test_failedValidation eliot/tests/test_output.py::MemoryLoggerTests::test_flushTracebacksNoTestFailure eliot/tests/test_output.py::MemoryLoggerTests::test_flushTracebacksReturnsExceptions eliot/tests/test_output.py::MemoryLoggerTests::test_flushTracebacksUnflushedTestFailure eliot/tests/test_output.py::MemoryLoggerTests::test_flushTracebacksUnflushedUnreturned eliot/tests/test_output.py::MemoryLoggerTests::test_interface eliot/tests/test_output.py::MemoryLoggerTests::test_notStringFieldKeys eliot/tests/test_output.py::MemoryLoggerTests::test_reset eliot/tests/test_output.py::MemoryLoggerTests::test_serialize eliot/tests/test_output.py::MemoryLoggerTests::test_serializeCopies eliot/tests/test_output.py::MemoryLoggerTests::test_serializer eliot/tests/test_output.py::MemoryLoggerTests::test_threadSafeWrite eliot/tests/test_output.py::MemoryLoggerTests::test_tracebacksCauseTestFailure eliot/tests/test_output.py::MemoryLoggerTests::test_write eliot/tests/test_output.py::DestinationsTests::test_addGlobalFields eliot/tests/test_output.py::DestinationsTests::test_addGlobalFieldsCumulative eliot/tests/test_output.py::DestinationsTests::test_buffering eliot/tests/test_output.py::DestinationsTests::test_buffering_second_batch eliot/tests/test_output.py::DestinationsTests::test_destination_exception_continue eliot/tests/test_output.py::DestinationsTests::test_destination_exception_multiple_destinations eliot/tests/test_output.py::DestinationsTests::test_global_fields_buffering eliot/tests/test_output.py::DestinationsTests::test_remove eliot/tests/test_output.py::DestinationsTests::test_removeNonExistent eliot/tests/test_output.py::DestinationsTests::test_send eliot/tests/test_output.py::LoggerTests::test_destination_exception_caught eliot/tests/test_output.py::LoggerTests::test_destination_exception_caught_twice eliot/tests/test_output.py::LoggerTests::test_destination_multiple_exceptions_caught eliot/tests/test_output.py::LoggerTests::test_global eliot/tests/test_output.py::LoggerTests::test_interface eliot/tests/test_output.py::LoggerTests::test_passedInDictionaryUnmodified eliot/tests/test_output.py::LoggerTests::test_safe_unicode_dictionary eliot/tests/test_output.py::LoggerTests::test_safe_unicode_dictionary_fallback eliot/tests/test_output.py::LoggerTests::test_safe_unicode_dictionary_fallback_failure eliot/tests/test_output.py::LoggerTests::test_serializationErrorTraceback eliot/tests/test_output.py::LoggerTests::test_serializer eliot/tests/test_output.py::LoggerTests::test_write eliot/tests/test_output.py::PEP8Tests::test_flush_tracebacks eliot/tests/test_output.py::ToFileTests::test_bytes_values eliot/tests/test_output.py::ToFileTests::test_filedestination_custom_encoder eliot/tests/test_output.py::ToFileTests::test_filedestination_flushes eliot/tests/test_output.py::ToFileTests::test_filedestination_unwriteable_file eliot/tests/test_output.py::ToFileTests::test_filedestination_writes_json_bytes eliot/tests/test_output.py::ToFileTests::test_filedestination_writes_json_unicode eliot/tests/test_output.py::ToFileTests::test_to_file_adds_destination eliot/tests/test_output.py::ToFileTests::test_to_file_custom_encoder