diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index cc76b77..7f7c1d1 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -34,4 +34,4 @@ jobs:
 
     - name: Test
       run: |
-        pytest
+        PYTHONPATH=. pytest
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index fbca482..29ef555 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -9,7 +9,7 @@ repos:
       - id: end-of-file-fixer
       - id: trailing-whitespace
   - repo: https://github.com/psf/black
-    rev: 22.1.0
+    rev: 22.3.0
     hooks:
       - id: black
   - repo: https://gitlab.com/pycqa/flake8
diff --git a/lazy_loader/__init__.py b/lazy_loader/__init__.py
index b1962af..08896b7 100644
--- a/lazy_loader/__init__.py
+++ b/lazy_loader/__init__.py
@@ -71,8 +71,18 @@ def __getattr__(name):
         if name in submodules:
             return importlib.import_module(f"{package_name}.{name}")
         elif name in attr_to_modules:
-            submod = importlib.import_module(f"{package_name}.{attr_to_modules[name]}")
-            return getattr(submod, name)
+            submod_path = f"{package_name}.{attr_to_modules[name]}"
+            submod = importlib.import_module(submod_path)
+            attr = getattr(submod, name)
+
+            # If the attribute lives in a file (module) with the same
+            # name as the attribute, ensure that the attribute and *not*
+            # the module is accessible on the package.
+            if name == attr_to_modules[name]:
+                pkg = sys.modules[package_name]
+                pkg.__dict__[name] = attr
+
+            return attr
         else:
             raise AttributeError(f"No {package_name} attribute {name}")
 
diff --git a/tests/fake_pkg/__init__.py b/tests/fake_pkg/__init__.py
new file mode 100644
index 0000000..540fd73
--- /dev/null
+++ b/tests/fake_pkg/__init__.py
@@ -0,0 +1,5 @@
+import lazy_loader as lazy
+
+__getattr__, __lazy_dir__, __all__ = lazy.attach(
+    __name__, submod_attrs={"some_func": ["some_func"]}
+)
diff --git a/tests/fake_pkg/some_func.py b/tests/fake_pkg/some_func.py
new file mode 100644
index 0000000..10e99ed
--- /dev/null
+++ b/tests/fake_pkg/some_func.py
@@ -0,0 +1,3 @@
+def some_func():
+    """Function with same name as submodule."""
+    pass
diff --git a/tests/test_lazy_loader.py b/tests/test_lazy_loader.py
index f74009f..d1ee06c 100644
--- a/tests/test_lazy_loader.py
+++ b/tests/test_lazy_loader.py
@@ -94,3 +94,17 @@ def test_lazy_attach():
     for k, v in expected.items():
         if v is not None:
             assert locls[k] == v
+
+
+def test_attach_same_module_and_attr_name():
+    import fake_pkg
+
+    # Grab attribute twice, to ensure that importing it does not
+    # override function by module
+    assert isinstance(fake_pkg.some_func, types.FunctionType)
+    assert isinstance(fake_pkg.some_func, types.FunctionType)
+
+    # Ensure imports from submodule still work
+    from fake_pkg.some_func import some_func
+
+    assert isinstance(some_func, types.FunctionType)