diff --git a/docs/source/bot_methods.rst b/docs/source/inclusions/bot_methods.rst
similarity index 100%
rename from docs/source/bot_methods.rst
rename to docs/source/inclusions/bot_methods.rst
diff --git a/docs/source/inclusions/pool_size_tip.rst b/docs/source/inclusions/pool_size_tip.rst
new file mode 100644
index 000000000..53dd2b311
--- /dev/null
+++ b/docs/source/inclusions/pool_size_tip.rst
@@ -0,0 +1,10 @@
+.. tip::
+    When making requests to the Bot API in an asynchronous fashion (e.g. via
+    :attr:`block=False <telegram.ext.BaseHandler.block>`, :meth:`Application.create_task <telegram.ext.Application.create_task>`,
+    :meth:`~telegram.ext.ApplicationBuilder.concurrent_updates` or the :class:`~telegram.ext.JobQueue`), it can happen that more requests
+    are being made in parallel than there are connections in the pool.
+    If the number of requests is much higher than the number of connections, even setting
+    :meth:`~telegram.ext.ApplicationBuilder.pool_timeout` to a larger value may not always be enough to prevent pool
+    timeouts.
+    You should therefore set :meth:`~telegram.ext.ApplicationBuilder.concurrent_updates`, :meth:`~telegram.ext.ApplicationBuilder.connection_pool_size` and
+    :meth:`~telegram.ext.ApplicationBuilder.pool_timeout` to values that make sense for your setup.
\ No newline at end of file
diff --git a/telegram/_bot.py b/telegram/_bot.py
index 46c0cfa04..ce726a3e2 100644
--- a/telegram/_bot.py
+++ b/telegram/_bot.py
@@ -172,7 +172,7 @@ class Bot(TelegramObject, AbstractAsyncContextManager):
         private_key (:obj:`bytes`, optional): Private key for decryption of telegram passport data.
         private_key_password (:obj:`bytes`, optional): Password for above private key.
 
-    .. include:: bot_methods.rst
+    .. include:: inclusions/bot_methods.rst
 
     """
 
diff --git a/telegram/ext/_application.py b/telegram/ext/_application.py
index c4086ba7a..a28e13521 100644
--- a/telegram/ext/_application.py
+++ b/telegram/ext/_application.py
@@ -252,7 +252,7 @@ class Application(Generic[BT, CCT, UD, CD, BD, JQ], AbstractAsyncContextManager)
         if isinstance(concurrent_updates, int) and concurrent_updates < 0:
             raise ValueError("`concurrent_updates` must be a non-negative integer!")
         if concurrent_updates is True:
-            concurrent_updates = 4096
+            concurrent_updates = 256
         self._concurrent_updates_sem = asyncio.BoundedSemaphore(concurrent_updates or 1)
         self._concurrent_updates: int = concurrent_updates or 0
 
diff --git a/telegram/ext/_applicationbuilder.py b/telegram/ext/_applicationbuilder.py
index aa110910b..325b624d0 100644
--- a/telegram/ext/_applicationbuilder.py
+++ b/telegram/ext/_applicationbuilder.py
@@ -191,7 +191,7 @@ class ApplicationBuilder(Generic[BT, CCT, UD, CD, BD, JQ]):
             )
         else:
             connection_pool_size = (
-                DefaultValue.get_value(getattr(self, f"{prefix}connection_pool_size")) or 128
+                DefaultValue.get_value(getattr(self, f"{prefix}connection_pool_size")) or 256
             )
 
         timeouts = dict(
@@ -424,7 +424,9 @@ class ApplicationBuilder(Generic[BT, CCT, UD, CD, BD, JQ]):
     def connection_pool_size(self: BuilderType, connection_pool_size: int) -> BuilderType:
         """Sets the size of the connection pool for the
         :paramref:`~telegram.request.HTTPXRequest.connection_pool_size` parameter of
-        :attr:`telegram.Bot.request`. Defaults to ``128``.
+        :attr:`telegram.Bot.request`. Defaults to ``256``.
+
+        .. include:: inclusions/pool_size_tip.rst
 
         Args:
             connection_pool_size (:obj:`int`): The size of the connection pool.
@@ -504,6 +506,8 @@ class ApplicationBuilder(Generic[BT, CCT, UD, CD, BD, JQ]):
         :paramref:`~telegram.request.HTTPXRequest.pool_timeout` parameter of
         :attr:`telegram.Bot.request`. Defaults to :obj:`None`.
 
+        .. include:: inclusions/pool_size_tip.rst
+
         Args:
             pool_timeout (:obj:`float`): See
                 :paramref:`telegram.request.HTTPXRequest.pool_timeout` for more information.
@@ -770,11 +774,13 @@ class ApplicationBuilder(Generic[BT, CCT, UD, CD, BD, JQ]):
             that your bot does not (explicitly or implicitly) rely on updates being processed
             sequentially.
 
+        .. include:: inclusions/pool_size_tip.rst
+
         .. seealso:: :attr:`telegram.ext.Application.concurrent_updates`
 
         Args:
             concurrent_updates (:obj:`bool` | :obj:`int`): Passing :obj:`True` will allow for
-                ``4096`` updates to be processed concurrently. Pass an integer to specify a
+                ``256`` updates to be processed concurrently. Pass an integer to specify a
                 different number of updates that may be processed concurrently.
 
         Returns:
diff --git a/tests/test_application.py b/tests/test_application.py
index 13c6f0738..5c7895ada 100644
--- a/tests/test_application.py
+++ b/tests/test_application.py
@@ -139,7 +139,7 @@ class TestApplication:
         assert recwarn[0].filename == __file__, "stacklevel is incorrect!"
 
     @pytest.mark.parametrize(
-        "concurrent_updates, expected", [(0, 0), (4, 4), (False, 0), (True, 4096)]
+        "concurrent_updates, expected", [(0, 0), (4, 4), (False, 0), (True, 256)]
     )
     @pytest.mark.filterwarnings("ignore: `Application` instances should")
     def test_init(self, bot, concurrent_updates, expected):
diff --git a/tests/test_applicationbuilder.py b/tests/test_applicationbuilder.py
index a2e0e5361..095a66137 100644
--- a/tests/test_applicationbuilder.py
+++ b/tests/test_applicationbuilder.py
@@ -93,7 +93,7 @@ class TestApplicationBuilder:
         )
 
         client = app.bot.request._client
-        assert client.limits == httpx.Limits(max_connections=128, max_keepalive_connections=128)
+        assert client.limits == httpx.Limits(max_connections=256, max_keepalive_connections=256)
         assert client.proxies is None
         assert client.timeout == httpx.Timeout(connect=5.0, read=5.0, write=5.0, pool=1.0)