diff --git a/Lib/mailbox.py b/Lib/mailbox.py
index 8b00460..73fe7d6 100644
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -1443,9 +1443,9 @@
                     line = line[:-1] + b'\n'
                 self._file.write(line.replace(b'\n', linesep))
                 if line == b'\n' or not line:
-                    self._file.write(b'*** EOOH ***' + linesep)
                     if first_pass:
                         first_pass = False
+                        self._file.write(b'*** EOOH ***' + linesep)
                         message.seek(original_pos)
                     else:
                         break
diff --git a/Lib/test/test_mailbox.py b/Lib/test/test_mailbox.py
index 9f1fdad..65120f7 100644
--- a/Lib/test/test_mailbox.py
+++ b/Lib/test/test_mailbox.py
@@ -148,20 +148,16 @@
             f.write(_bytes_sample_message)
             f.seek(0)
             key = self._box.add(f)
-        # See issue 11062
-        if not isinstance(self._box, mailbox.Babyl):
-            self.assertEqual(self._box.get_bytes(key).split(b'\n'),
-                _bytes_sample_message.split(b'\n'))
+        self.assertEqual(self._box.get_bytes(key).split(b'\n'),
+            _bytes_sample_message.split(b'\n'))
 
     def test_add_binary_nonascii_file(self):
         with tempfile.TemporaryFile('wb+') as f:
             f.write(self._non_latin_bin_msg)
             f.seek(0)
             key = self._box.add(f)
-        # See issue 11062
-        if not isinstance(self._box, mailbox.Babyl):
-            self.assertEqual(self._box.get_bytes(key).split(b'\n'),
-                self._non_latin_bin_msg.split(b'\n'))
+        self.assertEqual(self._box.get_bytes(key).split(b'\n'),
+            self._non_latin_bin_msg.split(b'\n'))
 
     def test_add_text_file_warns(self):
         with tempfile.TemporaryFile('w+') as f:
@@ -169,10 +165,8 @@
             f.seek(0)
             with self.assertWarns(DeprecationWarning):
                 key = self._box.add(f)
-        # See issue 11062
-        if not isinstance(self._box, mailbox.Babyl):
-            self.assertEqual(self._box.get_bytes(key).split(b'\n'),
-                _bytes_sample_message.split(b'\n'))
+        self.assertEqual(self._box.get_bytes(key).split(b'\n'),
+            _bytes_sample_message.split(b'\n'))
 
     def test_add_StringIO_warns(self):
         with self.assertWarns(DeprecationWarning):
diff --git a/Misc/NEWS b/Misc/NEWS
index 5d69e95..1e1e0c5 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -101,6 +101,8 @@
 Library
 -------
 
+- Issue #11062: Fix adding a message from file to Babyl mailbox.
+
 - Issue #15646: Prevent equivalent of a fork bomb when using
   multiprocessing on Windows without the "if __name__ == '__main__'"
   idiom.