diff --git a/Lib/tempfile.py b/Lib/tempfile.py
index 3ec6b4a..e3afa3b 100644
--- a/Lib/tempfile.py
+++ b/Lib/tempfile.py
@@ -578,8 +578,13 @@
     def tell(self):
         return self._file.tell()
 
-    def truncate(self):
-        self._file.truncate()
+    def truncate(self, size=None):
+        if size is None:
+            self._file.truncate()
+        else:
+            if size > self._max_size:
+                self.rollover()
+            self._file.truncate(size)
 
     def write(self, s):
         file = self._file
diff --git a/Lib/test/test_tempfile.py b/Lib/test/test_tempfile.py
index 014fca0..5b0bca7 100644
--- a/Lib/test/test_tempfile.py
+++ b/Lib/test/test_tempfile.py
@@ -846,6 +846,27 @@
                 pass
         self.assertRaises(ValueError, use_closed)
 
+    def test_truncate_with_size_parameter(self):
+        # A SpooledTemporaryFile can be truncated to zero size
+        f = tempfile.SpooledTemporaryFile(max_size=10)
+        f.write(b'abcdefg\n')
+        f.seek(0)
+        f.truncate()
+        self.assertFalse(f._rolled)
+        self.assertEqual(f._file.getvalue(), b'')
+        # A SpooledTemporaryFile can be truncated to a specific size
+        f = tempfile.SpooledTemporaryFile(max_size=10)
+        f.write(b'abcdefg\n')
+        f.truncate(4)
+        self.assertFalse(f._rolled)
+        self.assertEqual(f._file.getvalue(), b'abcd')
+        # A SpooledTemporaryFile rolls over if truncated to large size
+        f = tempfile.SpooledTemporaryFile(max_size=10)
+        f.write(b'abcdefg\n')
+        f.truncate(20)
+        self.assertTrue(f._rolled)
+        if has_stat:
+            self.assertEqual(os.fstat(f.fileno()).st_size, 20)
 
 test_classes.append(test_SpooledTemporaryFile)