diff --git a/Lib/test/test_zipfile64.py b/Lib/test/test_zipfile64.py
index 7d802d59849ce1..135ac5a06df011 100644
--- a/Lib/test/test_zipfile64.py
+++ b/Lib/test/test_zipfile64.py
@@ -15,6 +15,7 @@
 import time
 import tracemalloc
 import sys
+import io
 import unittest.mock as mock
 
 from tempfile import TemporaryFile
@@ -100,8 +101,9 @@ def setUp(self):
         # It will contain enough copies of self.data to reach about 8 GiB.
         self.datacount = 8*1024**3 // len(self.data)
 
-        # memory usage should not exceed 10 MiB
-        self.allowed_memory = 10*1024**2
+        # Memory usage should not exceed the default buffer size too
+        # much (10x as threshold)
+        self.allowed_memory = max(zipfile._REPACK_CHUNK_SIZE, io.DEFAULT_BUFFER_SIZE) * 10
 
     def _write_large_file(self, fh):
         next_time = time.monotonic() + _PRINT_WORKING_MSG_INTERVAL
@@ -201,7 +203,6 @@ def test_strip_removed_large_file_with_dd_no_sig(self):
         large file without causing a memory issue."""
         # Reduce data scale for this test, as it's especially slow...
         self.datacount = 30*1024**2 // len(self.data)
-        self.allowed_memory = 200*1024
 
         # Try the temp file.  If we do TESTFN2, then it hogs
         # gigabytes of disk space for the duration of the test.