diff --git a/CHANGES.rst b/CHANGES.rst
index f3e2cdb88..952a975bb 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -20,6 +20,10 @@ development at the same time, such as 4.5.x and 5.0.
 Unreleased
 ----------
 
+- Fix a failure when combining data files due to file names containing
+  glob-like patterns (`pull 1405`_).  Thanks, Michael Krebs and Benjamin
+  Schubert.
+
 - Fix a messaging failure when combining Windows data files on a different
   drive than the current directory. (`pull 1430`_, fixing `issue 1428`_).
   Thanks, Lorenzo Micò.
@@ -32,6 +36,7 @@ Unreleased
 
 .. _issue 972: https://github.com/nedbat/coveragepy/issues/972
 .. _pull 1347: https://github.com/nedbat/coveragepy/pull/1347
+.. _pull 1405: https://github.com/nedbat/coveragepy/issues/1405
 .. _pull 1413: https://github.com/nedbat/coveragepy/issues/1413
 .. _pull 1428: https://github.com/nedbat/coveragepy/issues/1428
 .. _pull 1430: https://github.com/nedbat/coveragepy/pull/1430
diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt
index d4a1e760f..4c6dfaf15 100644
--- a/CONTRIBUTORS.txt
+++ b/CONTRIBUTORS.txt
@@ -23,6 +23,7 @@ Artem Dayneko
 Arthur Deygin
 Ben Carlsson
 Ben Finney
+Benjamin Schubert
 Bernát Gábor
 Bill Hart
 Bradley Burns
@@ -111,6 +112,7 @@ Matthew Boehm
 Matthew Desmarais
 Matus Valo
 Max Linke
+Michael Krebs
 Michał Bultrowicz
 Mickie Betz
 Mike Fiedler
diff --git a/tests/test_data.py b/tests/test_data.py
index 3cb519ca4..8f05ada0d 100644
--- a/tests/test_data.py
+++ b/tests/test_data.py
@@ -878,6 +878,33 @@ def test_interleaved_erasing_bug716(self):
         # "no such table: meta"
         covdata2.add_lines(LINES_1)
 
+    @pytest.mark.parametrize(
+        "dpart, fpart",
+        [
+            ("", "[b-a]"),
+            ("[3-1]", ""),
+            ("[3-1]", "[b-a]"),
+        ],
+    )
+    def test_combining_with_crazy_filename(self, dpart, fpart):
+        dirname = f"py{dpart}"
+        basename = f"{dirname}/.coverage{fpart}"
+        os.makedirs(dirname)
+
+        covdata1 = CoverageData(basename=basename, suffix="1")
+        covdata1.add_lines(LINES_1)
+        covdata1.write()
+
+        covdata2 = CoverageData(basename=basename, suffix="2")
+        covdata2.add_lines(LINES_2)
+        covdata2.write()
+
+        covdata3 = CoverageData(basename=basename)
+        combine_parallel_data(covdata3)
+        assert_line_counts(covdata3, SUMMARY_1_2)
+        assert_measured_files(covdata3, MEASURED_FILES_1_2)
+        self.assert_file_count(glob.escape(basename) + ".*", 0)
+
 
 class DumpsLoadsTest(CoverageTest):
     """Tests of CoverageData.dumps and loads."""