diff --git a/test/functional/swift_test_client.py b/test/functional/swift_test_client.py
index c6af80d1a2..ae00644d9c 100644
--- a/test/functional/swift_test_client.py
+++ b/test/functional/swift_test_client.py
@@ -111,6 +111,91 @@ def listing_items(method):
             items = []
 
 
+def putrequest(self, method, url, skip_host=False, skip_accept_encoding=False):
+    '''Send a request to the server.
+
+    This is mostly a regurgitation of CPython's HTTPConnection.putrequest,
+    but fixed up so we can still send arbitrary bytes in the request line
+    on py3. See also: https://bugs.python.org/issue36274
+
+    To use, swap out a HTTP(S)Connection's putrequest with something like::
+
+       conn.putrequest = putrequest.__get__(conn)
+
+    :param method: specifies an HTTP request method, e.g. 'GET'.
+    :param url: specifies the object being requested, e.g. '/index.html'.
+    :param skip_host: if True does not add automatically a 'Host:' header
+    :param skip_accept_encoding: if True does not add automatically an
+       'Accept-Encoding:' header
+    '''
+    # (Mostly) inline the HTTPConnection implementation; just fix it
+    # so we can send non-ascii request lines. For comparison, see
+    # https://github.com/python/cpython/blob/v2.7.16/Lib/httplib.py#L888-L1003
+    # and https://github.com/python/cpython/blob/v3.7.2/
+    # Lib/http/client.py#L1061-L1183
+    if self._HTTPConnection__response \
+            and self._HTTPConnection__response.isclosed():
+        self._HTTPConnection__response = None
+
+    if self._HTTPConnection__state == http_client._CS_IDLE:
+        self._HTTPConnection__state = http_client._CS_REQ_STARTED
+    else:
+        raise http_client.CannotSendRequest(self._HTTPConnection__state)
+
+    self._method = method
+    if not url:
+        url = '/'
+    self._path = url
+    request = '%s %s %s' % (method, url, self._http_vsn_str)
+    if not isinstance(request, bytes):
+        # This choice of encoding is the whole reason we copy/paste from
+        # cpython. When making backend requests, it should never be
+        # necessary; however, we have some functional tests that want
+        # to send non-ascii bytes.
+        # TODO: when https://bugs.python.org/issue36274 is resolved, make
+        # sure we fix up our API to match whatever upstream chooses to do
+        self._output(request.encode('latin1'))
+    else:
+        self._output(request)
+
+    if self._http_vsn == 11:
+        if not skip_host:
+            netloc = ''
+            if url.startswith('http'):
+                nil, netloc, nil, nil, nil = urllib.parse.urlsplit(url)
+
+            if netloc:
+                try:
+                    netloc_enc = netloc.encode("ascii")
+                except UnicodeEncodeError:
+                    netloc_enc = netloc.encode("idna")
+                self.putheader('Host', netloc_enc)
+            else:
+                if self._tunnel_host:
+                    host = self._tunnel_host
+                    port = self._tunnel_port
+                else:
+                    host = self.host
+                    port = self.port
+
+                try:
+                    host_enc = host.encode("ascii")
+                except UnicodeEncodeError:
+                    host_enc = host.encode("idna")
+
+                if host.find(':') >= 0:
+                    host_enc = b'[' + host_enc + b']'
+
+                if port == self.default_port:
+                    self.putheader('Host', host_enc)
+                else:
+                    host_enc = host_enc.decode("ascii")
+                    self.putheader('Host', "%s:%s" % (host_enc, port))
+
+        if not skip_accept_encoding:
+            self.putheader('Accept-Encoding', 'identity')
+
+
 class Connection(object):
     def __init__(self, config):
         for key in 'auth_host auth_port auth_ssl username password'.split():
@@ -132,6 +217,7 @@ class Connection(object):
         self.storage_netloc = None
         self.storage_path = None
         self.conn_class = None
+        self.connection = None  # until you call .http_connect()
 
     @property
     def storage_url(self):
@@ -235,6 +321,7 @@ class Connection(object):
                 context=ssl._create_unverified_context())
         else:
             self.connection = self.conn_class(self.storage_netloc)
+        self.connection.putrequest = putrequest.__get__(self.connection)
 
     def make_path(self, path=None, cfg=None):
         if path is None: