diff --git a/coverage/python.py b/coverage/python.py
index 089c27ea6..057cd6061 100644
--- a/coverage/python.py
+++ b/coverage/python.py
@@ -244,9 +244,6 @@ def should_be_python(self) -> bool:
         # Anything named *.py* should be Python.
         if ext.startswith(".py"):
             return True
-        # A file with no extension should be Python.
-        if not ext:
-            return True
         # Everything else is probably not Python.
         return False
 
diff --git a/tests/test_filereporter.py b/tests/test_filereporter.py
index c36fa013b..b273d6193 100644
--- a/tests/test_filereporter.py
+++ b/tests/test_filereporter.py
@@ -102,3 +102,10 @@ def test_zipfile(self) -> None:
         z1z1 = PythonFileReporter(zip1.zip1)
         assert z1.source() == ""
         assert "# My zip file!" in z1z1.source().splitlines()
+
+    def test_python_extensions(self) -> None:
+        f1 = PythonFileReporter("afile.py")
+        f2 = PythonFileReporter("Makefile")
+
+        assert f1.should_be_python()
+        assert not f2.should_be_python()