diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 1394a26f2096ff..6363211328f386 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -2896,12 +2896,12 @@ def next(self):
             except Exception as e:
                 try:
                     import zlib
+                except ImportError:
+                    pass
+                else:
                     if isinstance(e, zlib.error):
                         raise ReadError(f'zlib error: {e}') from None
-                    else:
-                        raise e
-                except ImportError:
-                    raise e
+                raise
             break
 
         if tarinfo is not None:
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 192c948edc6056..cccc96eb6feb01 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -829,6 +829,27 @@ def test_zlib_error_does_not_leak(self):
             with self.assertRaises(tarfile.ReadError):
                 tarfile.open(self.tarname)
 
+    def test_next_preserves_exception_traceback(self):
+        class ExpectedError(Exception):
+            pass
+
+        class FailingFile(io.BytesIO):
+            def read(self, *args):
+                raise ExpectedError()
+
+        with self.assertRaises(ExpectedError) as cm:
+            tarfile.open(fileobj=FailingFile(), mode="r:")
+
+        next_frames = []
+        tb = cm.exception.__traceback__
+        while tb is not None:
+            code = tb.tb_frame.f_code
+            if (code.co_filename == tarfile.__file__
+                    and code.co_name == "next"):
+                next_frames.append(tb.tb_lineno)
+            tb = tb.tb_next
+        self.assertEqual(len(next_frames), 1)
+
     def test_next_on_empty_tarfile(self):
         fd = io.BytesIO()
         tf = tarfile.open(fileobj=fd, mode="w")