diff --git a/Lib/test/test_email/test_email.py b/Lib/test/test_email/test_email.py
--- a/Lib/test/test_email/test_email.py
+++ b/Lib/test/test_email/test_email.py
@@ -10,6 +10,7 @@
 
 from io import StringIO, BytesIO
 from itertools import chain
+from random import choice
 
 import email
 import email.policy
@@ -3364,6 +3365,28 @@
         self.assertEqual(''.join([il for il, n in imt]), ''.join(om))
 
 
+    def test_push_random(self):
+        from email.feedparser import BufferedSubFile, NeedMoreData
+
+        n = 10000
+        chunksize = 5
+        chars = 'abcd \t\r\n'
+
+        s = ''.join(choice(chars) for i in range(n)) + '\n'
+        target = s.splitlines(True)
+
+        bsf = BufferedSubFile()
+        lines = []
+        for i in range(0, n+1, chunksize):
+            chunk = s[i:i+chunksize]
+            bsf.push(chunk)
+            while True:
+                ol = bsf.readline()
+                if ol == NeedMoreData:
+                    break
+                lines.append(ol)
+        self.assertEqual(lines, target)
+
 
 class TestParsers(TestEmailBase):