diff --git a/ds-caselaw-ingester/lambda_function.py b/ds-caselaw-ingester/lambda_function.py
index df3e389..3c8890f 100644
--- a/ds-caselaw-ingester/lambda_function.py
+++ b/ds-caselaw-ingester/lambda_function.py
@@ -159,6 +159,16 @@ class DocumentInsertionError(ReportableException):
     pass
 
 
+def modify_filename(original: str, addition: str) -> str:
+    "Add an addition after the filename, so TRE-2024-A.tar.gz becomes TRE-2024-A_nodocx.tar.gz"
+    path, basename = os.path.split(original)
+    # dot will be an empty string if there is no dot in the filename.
+    # prefix will be everything upto and not including the first dot.
+    prefix, dot, suffix = basename.partition(".")
+    new_basename = f"{prefix}{addition}{dot}{suffix}"
+    return os.path.join(path, new_basename)
+
+
 def all_messages(event) -> List[Message]:
     """All the messages in the SNS event, as Message subclasses"""
     decoder = json.decoder.JSONDecoder()
@@ -505,12 +515,23 @@ def process_message(message):
     if has_TDR_data:
         store_metadata(uri, metadata)
 
+    # Determine if there's a word document -- we need to know before we save the tar.gz file
+    docx_filename = extract_docx_filename(metadata, consignment_reference)
+    print(f"extracted docx filename is {docx_filename!r}")
+
     # Copy original tarfile
-    store_file(open(filename, mode="rb"), uri, os.path.basename(filename), s3_client)
+    modified_targz_filename = (
+        filename if docx_filename else modify_filename(filename, "_nodocx")
+    )
+    store_file(
+        open(modified_targz_filename, mode="rb"),
+        uri,
+        os.path.basename(filename),
+        s3_client,
+    )
+    print(f"saved tar.gz as {modified_targz_filename!r}")
 
     # Store docx and rename
-    docx_filename = extract_docx_filename(metadata, consignment_reference)
-    print(f"extracted docx filename is {docx_filename!r}")
     # The docx_filename is None for files which have been reparsed.
     if docx_filename is not None:
         copy_file(
diff --git a/ds-caselaw-ingester/tests.py b/ds-caselaw-ingester/tests.py
index 35c47b6..6c93457 100644
--- a/ds-caselaw-ingester/tests.py
+++ b/ds-caselaw-ingester/tests.py
@@ -81,8 +81,10 @@ class TestHandler:
     @patch("lambda_function.send_updated_judgment_notification")
     @patch("lambda_function.send_new_judgment_notification")
     @patch("lambda_function.VersionAnnotation")
+    @patch("lambda_function.modify_filename")
     def test_handler_messages_v2(
         self,
+        modify_filename,
         annotation,
         notify_new,
         notify_update,
@@ -114,6 +116,8 @@ def test_handler_messages_v2(
         notify_update.assert_called()
         assert notify_update.call_count == 2
         notify_new.assert_not_called()
+        modify_filename.assert_not_called()
+
         annotation.assert_called_with(
             ANY,
             automated=False,
@@ -127,8 +131,10 @@ def test_handler_messages_v2(
     @patch("lambda_function.send_new_judgment_notification")
     @patch("lambda_function.send_updated_judgment_notification")
     @patch("lambda_function.VersionAnnotation")
+    @patch("lambda_function.modify_filename")
     def test_handler_messages_s3(
         self,
+        modify_filename,
         annotation,
         notify_new,
         notify_updated,
@@ -161,6 +167,7 @@ def test_handler_messages_s3(
         assert apiclient.set_published.call_count == 2
         notify_new.assert_not_called()
         notify_updated.assert_not_called()
+        modify_filename.assert_not_called()
         annotation.assert_called_with(
             ANY,
             automated=True,
@@ -820,3 +827,18 @@ def test_unquote_s3(self, getenv, os):
         mock_s3_client.download_file.assert_called_with(
             ANY, "2010 Reported/[2010]/1.tar.gz", ANY
         )
+
+
+modify_filename_data = [
+    ["TRE-2023-XYZ.tar.gz", "TRE-2023-XYZ_.tar.gz"],
+    ["/a/b/c.d.e", "/a/b/c_.d.e"],
+    [
+        "",
+        "_",
+    ],
+]
+
+
+@pytest.mark.parametrize("was, now", modify_filename_data)
+def test_modify_targz_filename(was, now):
+    assert lambda_function.modify_filename(was, addition="_") == now