diff --git a/docker/api/container.py b/docker/api/container.py
index 9cc14dbd..b8507d85 100644
--- a/docker/api/container.py
+++ b/docker/api/container.py
@@ -15,12 +15,18 @@ class ContainerApiMixin(object):
             'logs': logs and 1 or 0,
             'stdout': stdout and 1 or 0,
             'stderr': stderr and 1 or 0,
-            'stream': stream and 1 or 0,
+            'stream': stream and 1 or 0
         }
+
+        headers = {
+            'Connection': 'Upgrade',
+            'Upgrade': 'tcp'
+        }
+
         u = self._url("/containers/{0}/attach", container)
-        response = self._post(u, params=params, stream=stream)
+        response = self._post(u, headers=headers, params=params, stream=stream)
 
-        return self._get_result(container, stream, response)
+        return self._read_from_socket(response, stream)
 
     @utils.check_resource
     def attach_socket(self, container, params=None, ws=False):
@@ -34,9 +40,18 @@ class ContainerApiMixin(object):
         if ws:
             return self._attach_websocket(container, params)
 
+        headers = {
+            'Connection': 'Upgrade',
+            'Upgrade': 'tcp'
+        }
+
         u = self._url("/containers/{0}/attach", container)
-        return self._get_raw_response_socket(self.post(
-            u, None, params=self._attach_params(params), stream=True))
+        return self._get_raw_response_socket(
+            self.post(
+                u, None, params=self._attach_params(params), stream=True,
+                headers=headers
+            )
+        )
 
     @utils.check_resource
     def commit(self, container, repository=None, tag=None, message=None,
diff --git a/docker/api/exec_api.py b/docker/api/exec_api.py
index f0e4afa6..6e499960 100644
--- a/docker/api/exec_api.py
+++ b/docker/api/exec_api.py
@@ -56,8 +56,6 @@ class ExecApiMixin(object):
     def exec_start(self, exec_id, detach=False, tty=False, stream=False,
                    socket=False):
         # we want opened socket if socket == True
-        if socket:
-            stream = True
         if isinstance(exec_id, dict):
             exec_id = exec_id.get('Id')
 
@@ -66,10 +64,18 @@ class ExecApiMixin(object):
             'Detach': detach
         }
 
+        headers = {} if detach else {
+            'Connection': 'Upgrade',
+            'Upgrade': 'tcp'
+        }
+
         res = self._post_json(
-            self._url('/exec/{0}/start', exec_id), data=data, stream=stream
+            self._url('/exec/{0}/start', exec_id),
+            headers=headers,
+            data=data,
+            stream=True
         )
 
         if socket:
             return self._get_raw_response_socket(res)
-        return self._get_result_tty(stream, res, tty)
+        return self._read_from_socket(res, stream)
diff --git a/docker/client.py b/docker/client.py
index b96a78ce..6ca9e57a 100644
--- a/docker/client.py
+++ b/docker/client.py
@@ -29,6 +29,7 @@ from .ssladapter import ssladapter
 from .tls import TLSConfig
 from .transport import UnixAdapter
 from .utils import utils, check_resource, update_headers, kwargs_from_env
+from .utils.socket import frames_iter
 try:
     from .transport import NpipeAdapter
 except ImportError:
@@ -305,6 +306,14 @@ class Client(
         for out in response.iter_content(chunk_size=1, decode_unicode=True):
             yield out
 
+    def _read_from_socket(self, response, stream):
+        socket = self._get_raw_response_socket(response)
+
+        if stream:
+            return frames_iter(socket)
+        else:
+            return six.binary_type().join(frames_iter(socket))
+
     def _disable_socket_timeout(self, socket):
         """ Depending on the combination of python version and whether we're
         connecting over http or https, we might need to access _sock, which
diff --git a/docker/utils/socket.py b/docker/utils/socket.py
new file mode 100644
index 00000000..ed343507
--- /dev/null
+++ b/docker/utils/socket.py
@@ -0,0 +1,68 @@
+import errno
+import os
+import select
+import struct
+
+import six
+
+
+class SocketError(Exception):
+    pass
+
+
+def read(socket, n=4096):
+    """
+    Reads at most n bytes from socket
+    """
+    recoverable_errors = (errno.EINTR, errno.EDEADLK, errno.EWOULDBLOCK)
+
+    # wait for data to become available
+    select.select([socket], [], [])
+
+    try:
+        if hasattr(socket, 'recv'):
+            return socket.recv(n)
+        return os.read(socket.fileno(), n)
+    except EnvironmentError as e:
+        if e.errno not in recoverable_errors:
+            raise
+
+
+def read_exactly(socket, n):
+    """
+    Reads exactly n bytes from socket
+    Raises SocketError if there isn't enough data
+    """
+    data = six.binary_type()
+    while len(data) < n:
+        next_data = read(socket, n - len(data))
+        if not next_data:
+            raise SocketError("Unexpected EOF")
+        data += next_data
+    return data
+
+
+def next_frame_size(socket):
+    """
+    Returns the size of the next frame of data waiting to be read from socket,
+    according to the protocol defined here:
+
+    https://docs.docker.com/engine/reference/api/docker_remote_api_v1.24/#/attach-to-a-container
+    """
+    try:
+        data = read_exactly(socket, 8)
+    except SocketError:
+        return 0
+
+    _, actual = struct.unpack('>BxxxL', data)
+    return actual
+
+
+def frames_iter(socket):
+    """
+    Returns a generator of frames read from socket
+    """
+    n = next_frame_size(socket)
+    while n > 0:
+        yield read(socket, n)
+        n = next_frame_size(socket)

diff --git a/tests/helpers.py b/tests/helpers.py
index 21036ace..94ea3887 100644
--- a/tests/helpers.py
+++ b/tests/helpers.py
@@ -1,9 +1,6 @@
-import errno
 import os
 import os.path
-import select
 import shutil
-import struct
 import tarfile
 import tempfile
 import unittest
@@ -54,7 +51,7 @@ def exec_driver_is_native():
         c = docker_client()
         EXEC_DRIVER = c.info()['ExecutionDriver']
         c.close()
-    return EXEC_DRIVER.startswith('native')
+    return EXEC_DRIVER.startswith('native') or EXEC_DRIVER == ''
 
 
 def docker_client(**kwargs):
@@ -67,49 +64,6 @@ def docker_client_kwargs(**kwargs):
     return client_kwargs
 
 
-def read_socket(socket, n=4096):
-    """ Code stolen from dockerpty to read the socket """
-    recoverable_errors = (errno.EINTR, errno.EDEADLK, errno.EWOULDBLOCK)
-
-    # wait for data to become available
-    select.select([socket], [], [])
-
-    try:
-        if hasattr(socket, 'recv'):
-            return socket.recv(n)
-        return os.read(socket.fileno(), n)
-    except EnvironmentError as e:
-        if e.errno not in recoverable_errors:
-            raise
-
-
-def next_packet_size(socket):
-    """ Code stolen from dockerpty to get the next packet size """
-    data = six.binary_type()
-    while len(data) < 8:
-        next_data = read_socket(socket, 8 - len(data))
-        if not next_data:
-            return 0
-        data = data + next_data
-
-    if data is None:
-        return 0
-
-    if len(data) == 8:
-        _, actual = struct.unpack('>BxxxL', data)
-        return actual
-
-
-def read_data(socket, packet_size):
-    data = six.binary_type()
-    while len(data) < packet_size:
-        next_data = read_socket(socket, packet_size - len(data))
-        if not next_data:
-            assert False, "Failed trying to read in the dataz"
-        data += next_data
-    return data
-
-
 class BaseTestCase(unittest.TestCase):
     tmp_imgs = []
     tmp_containers = []
diff --git a/tests/integration/container_test.py b/tests/integration/container_test.py
index 56b648a3..61b33983 100644
--- a/tests/integration/container_test.py
+++ b/tests/integration/container_test.py
@@ -3,6 +3,8 @@ import signal
 import tempfile
 
 import docker
+from docker.utils.socket import next_frame_size
+from docker.utils.socket import read_exactly
 import pytest
 import six
 
@@ -1025,9 +1027,9 @@ class AttachContainerTest(helpers.BaseTestCase):
 
         self.client.start(ident)
 
-        next_size = helpers.next_packet_size(pty_stdout)
+        next_size = next_frame_size(pty_stdout)
         self.assertEqual(next_size, len(line))
-        data = helpers.read_data(pty_stdout, next_size)
+        data = read_exactly(pty_stdout, next_size)
         self.assertEqual(data.decode('utf-8'), line)
 
 
diff --git a/tests/integration/exec_test.py b/tests/integration/exec_test.py
index 9f548080..8bf2762a 100644
--- a/tests/integration/exec_test.py
+++ b/tests/integration/exec_test.py
@@ -1,5 +1,8 @@
 import pytest
 
+from docker.utils.socket import next_frame_size
+from docker.utils.socket import read_exactly
+
 from .. import helpers
 
 BUSYBOX = helpers.BUSYBOX
@@ -107,9 +110,9 @@ class ExecTest(helpers.BaseTestCase):
         socket = self.client.exec_start(exec_id, socket=True)
         self.addCleanup(socket.close)
 
-        next_size = helpers.next_packet_size(socket)
+        next_size = next_frame_size(socket)
         self.assertEqual(next_size, len(line))
-        data = helpers.read_data(socket, next_size)
+        data = read_exactly(socket, next_size)
         self.assertEqual(data.decode('utf-8'), line)
 
     def test_exec_inspect(self):
diff --git a/tests/unit/api_test.py b/tests/unit/api_test.py
index 23fd1913..34bf14f6 100644
--- a/tests/unit/api_test.py
+++ b/tests/unit/api_test.py
@@ -93,6 +93,10 @@ def fake_put(self, url, *args, **kwargs):
 def fake_delete(self, url, *args, **kwargs):
     return fake_request('DELETE', url, *args, **kwargs)
 
+
+def fake_read_from_socket(self, response, stream):
+    return six.binary_type()
+
 url_base = 'http+docker://localunixsocket/'
 url_prefix = '{0}v{1}/'.format(
     url_base,
@@ -103,7 +107,8 @@ class DockerClientTest(base.Cleanup, base.BaseTestCase):
     def setUp(self):
         self.patcher = mock.patch.multiple(
             'docker.Client', get=fake_get, post=fake_post, put=fake_put,
-            delete=fake_delete
+            delete=fake_delete,
+            _read_from_socket=fake_read_from_socket
         )
         self.patcher.start()
         self.client = docker.Client()
diff --git a/tests/unit/exec_test.py b/tests/unit/exec_test.py
index 3007799c..6ba2a3dd 100644
--- a/tests/unit/exec_test.py
+++ b/tests/unit/exec_test.py
@@ -51,8 +51,36 @@ class ExecTest(DockerClientTest):
             }
         )
 
-        self.assertEqual(args[1]['headers'],
-                         {'Content-Type': 'application/json'})
+        self.assertEqual(
+            args[1]['headers'], {
+                'Content-Type': 'application/json',
+                'Connection': 'Upgrade',
+                'Upgrade': 'tcp'
+            }
+        )
+
+    def test_exec_start_detached(self):
+        self.client.exec_start(fake_api.FAKE_EXEC_ID, detach=True)
+
+        args = fake_request.call_args
+        self.assertEqual(
+            args[0][1], url_prefix + 'exec/{0}/start'.format(
+                fake_api.FAKE_EXEC_ID
+            )
+        )
+
+        self.assertEqual(
+            json.loads(args[1]['data']), {
+                'Tty': False,
+                'Detach': True
+            }
+        )
+
+        self.assertEqual(
+            args[1]['headers'], {
+                'Content-Type': 'application/json'
+            }
+        )
 
     def test_exec_inspect(self):
         self.client.exec_inspect(fake_api.FAKE_EXEC_ID)

The api client should send connection upgrade headers
To hint proxies about connection hijacking, docker clients should send connection upgrade headers like the docker cli does.

From https://docs.docker.com/engine/reference/api/docker_remote_api_v1.24/#/4-2-hijacking:

> In this version of the API, /attach, uses hijacking to transport stdin, stdout, and stderr on the same socket.
>
> To hint potential proxies about connection hijacking, Docker client sends connection upgrade headers similarly to websocket.

```
Upgrade: tcp
Connection: Upgrade
```

On Docker for Desktop, the proxy that sits between Docker Compose and the daemon will not be aware that the connection will be hijacked. This can lead to an issue where the proxy will install a CloseNotifier and just after that will hijack the connection, which is know to be incompatible. See https://github.com/docker/compose/issues/3685

See also https://github.com/docker/compose/issues/3700

tests/unit/api_test.py::DockerApiTest::test_auto_retrieve_server_version tests/unit/api_test.py::DockerApiTest::test_create_host_config_secopt tests/unit/api_test.py::DockerApiTest::test_ctor tests/unit/api_test.py::DockerApiTest::test_events tests/unit/api_test.py::DockerApiTest::test_events_with_filters tests/unit/api_test.py::DockerApiTest::test_events_with_since_until tests/unit/api_test.py::DockerApiTest::test_info tests/unit/api_test.py::DockerApiTest::test_remove_link tests/unit/api_test.py::DockerApiTest::test_retrieve_server_version tests/unit/api_test.py::DockerApiTest::test_search tests/unit/api_test.py::DockerApiTest::test_url_compatibility_http tests/unit/api_test.py::DockerApiTest::test_url_compatibility_http_unix_triple_slash tests/unit/api_test.py::DockerApiTest::test_url_compatibility_tcp tests/unit/api_test.py::DockerApiTest::test_url_compatibility_unix tests/unit/api_test.py::DockerApiTest::test_url_compatibility_unix_triple_slash tests/unit/api_test.py::DockerApiTest::test_url_invalid_resource tests/unit/api_test.py::DockerApiTest::test_url_no_resource tests/unit/api_test.py::DockerApiTest::test_url_unversioned_api tests/unit/api_test.py::DockerApiTest::test_url_valid_resource tests/unit/api_test.py::DockerApiTest::test_version tests/unit/api_test.py::DockerApiTest::test_version_no_api_version tests/unit/exec_test.py::ExecTest::test_exec_create tests/unit/exec_test.py::ExecTest::test_exec_inspect tests/unit/exec_test.py::ExecTest::test_exec_resize tests/unit/exec_test.py::ExecTest::test_exec_start tests/unit/exec_test.py::ExecTest::test_exec_start_detached