diff --git a/Lib/test/test_xml_etree.py b/Lib/test/test_xml_etree.py
index d90f9780c52..da1ad096868 100644
--- a/Lib/test/test_xml_etree.py
+++ b/Lib/test/test_xml_etree.py
@@ -2286,6 +2286,15 @@ def test_write_to_user_binary_writer_with_bom(self):
                 '''<?xml version='1.0' encoding='utf-16'?>\n'''
                 '''<site />'''.encode("utf-16"))
 
+    def test_tostringlist_invariant(self):
+        root = ET.fromstring('<tag>foo</tag>')
+        self.assertEqual(
+            ET.tostring(root, 'unicode'),
+            ''.join(ET.tostringlist(root, 'unicode')))
+        self.assertEqual(
+            ET.tostring(root, 'utf-16'),
+            b''.join(ET.tostringlist(root, 'utf-16')))
+
 
 class ParseErrorTest(unittest.TestCase):
     def test_subclass(self):
diff --git a/Lib/xml/etree/ElementTree.py b/Lib/xml/etree/ElementTree.py
index 10bf84992ed..3981659dd93 100644
--- a/Lib/xml/etree/ElementTree.py
+++ b/Lib/xml/etree/ElementTree.py
@@ -1190,9 +1190,15 @@ class DataStream(io.BufferedIOBase):
         def writable(self):
             return True
 
+        def seekable(self):
+            return True
+
         def write(self, b):
             data.append(b)
 
+        def tell(self):
+            return len(data)
+
     ElementTree(element).write(DataStream(), encoding, method=method)
     return data