diff --git a/Lib/email/contentmanager.py b/Lib/email/contentmanager.py
index b904ded94c9..2b4b8757f46 100644
--- a/Lib/email/contentmanager.py
+++ b/Lib/email/contentmanager.py
@@ -146,13 +146,13 @@ def _encode_text(string, charset, cte, policy):
     def normal_body(lines): return b'\n'.join(lines) + b'\n'
     if cte==None:
         # Use heuristics to decide on the "best" encoding.
-        try:
-            return '7bit', normal_body(lines).decode('ascii')
-        except UnicodeDecodeError:
-            pass
-        if (policy.cte_type == '8bit' and
-                max(len(x) for x in lines) <= policy.max_line_length):
-            return '8bit', normal_body(lines).decode('ascii', 'surrogateescape')
+        if max(len(x) for x in lines) <= policy.max_line_length:
+            try:
+                return '7bit', normal_body(lines).decode('ascii')
+            except UnicodeDecodeError:
+                pass
+            if policy.cte_type == '8bit':
+                return '8bit', normal_body(lines).decode('ascii', 'surrogateescape')
         sniff = embedded_body(lines[:10])
         sniff_qp = quoprimime.body_encode(sniff.decode('latin-1'),
                                           policy.max_line_length)
diff --git a/Lib/test/test_email/test_contentmanager.py b/Lib/test/test_email/test_contentmanager.py
index 169058eac83..64dca2d017e 100644
--- a/Lib/test/test_email/test_contentmanager.py
+++ b/Lib/test/test_email/test_contentmanager.py
@@ -329,6 +329,21 @@ class TestRawDataManager(TestEmailBase):
         self.assertEqual(m.get_payload(decode=True).decode('utf-8'), content)
         self.assertEqual(m.get_content(), content)
 
+    def test_set_text_plain_long_line_heuristics(self):
+        m = self._make_message()
+        content = ("Simple but long message that is over 78 characters"
+                   " long to force transfer encoding.\n")
+        raw_data_manager.set_content(m, content)
+        self.assertEqual(str(m), textwrap.dedent("""\
+            Content-Type: text/plain; charset="utf-8"
+            Content-Transfer-Encoding: quoted-printable
+
+            Simple but long message that is over 78 characters long to =
+            force transfer encoding.
+            """))
+        self.assertEqual(m.get_payload(decode=True).decode('utf-8'), content)
+        self.assertEqual(m.get_content(), content)
+
     def test_set_text_short_line_minimal_non_ascii_heuristics(self):
         m = self._make_message()
         content = "et là il est monté sur moi et il commence à m'éto.\n"
diff --git a/Misc/NEWS.d/next/Library/2020-05-11-19-17-23.bpo-40597.4SGfgm.rst b/Misc/NEWS.d/next/Library/2020-05-11-19-17-23.bpo-40597.4SGfgm.rst
new file mode 100644
index 00000000000..1b9fe609c25
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-11-19-17-23.bpo-40597.4SGfgm.rst
@@ -0,0 +1 @@
+If text content lines are longer than policy.max_line_length, always use a content-encoding to make sure they are wrapped.