diff --git a/debian/changelog b/debian/changelog
index 889ef7bb73a302de716f744513da14a249d680d9..5aff953b7d6ebb99b1ebff87078998c30c436ac5 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -3,6 +3,7 @@ dh-python (6.20240402) UNRELEASED; urgency=medium
   * Add support for Python 3.11 and 3.12 in test_interpreter.
   * Add generic test for the current default Python 3 interpreter in
     test_interpreter.
+  * dh_python3: Don't rename _module to module. (Closes: #1068255)
 
  -- Stefano Rivera <stefanor@debian.org>  Mon, 22 Apr 2024 18:33:09 -0400
 
diff --git a/dhpython/interpreter.py b/dhpython/interpreter.py
index 517b0790a455b9b36dbb0989bab77ef8ca428487..2e1c06d5241b755db05acf85c2face3a16c5110b 100644
--- a/dhpython/interpreter.py
+++ b/dhpython/interpreter.py
@@ -450,7 +450,9 @@ class Interpreter:
         tmp_multiarch = info['multiarch'] or multiarch
 
         result = info['name']
-        if result.endswith('module') and result != 'module' and self.impl == 'cpython3':
+        if (result.endswith('module')
+                and result not in ('module', '_module')
+                and self.impl == 'cpython3'):
             result = result[:-6]
 
         if tmp_soabi:
diff --git a/tests/test_interpreter.py b/tests/test_interpreter.py
index f1cf55b1848a4f46dc532d7865989c301068cce4..7f7dacdb4b69a64848b4e1803467579b7a2601f6 100644
--- a/tests/test_interpreter.py
+++ b/tests/test_interpreter.py
@@ -261,5 +261,12 @@ class TestInterpreter(unittest.TestCase):
         self.assertIsNone(i.check_extname('foo.abi3.so'))
         self.assertEqual(i.check_extname('foo/bar/bazmodule.so'), rf'foo/bar/baz.cpython-{pyver}d-MYARCH.so')
 
+    def test_bare_module(self):
+        i = Interpreter('python{}.{}'.format(*sys.version_info[:2]))
+        pyver = '{}{}'.format(*sys.version_info[:2])
+        self.assertEqual(i.check_extname('module.so'), rf'module.cpython-{pyver}-MYARCH.so')
+        self.assertEqual(i.check_extname('_module.so'), rf'_module.cpython-{pyver}-MYARCH.so')
+
+
 if __name__ == '__main__':
     unittest.main()