diff --git a/src/lazy_loader/__init__.py b/src/lazy_loader/__init__.py
index 23b5382..8448ee6 100644
--- a/src/lazy_loader/__init__.py
+++ b/src/lazy_loader/__init__.py
@@ -21,7 +21,12 @@
 threadlock = threading.Lock()
 
 
-def attach(package_name, submodules=None, submod_attrs=None):
+def attach(
+    package_name,
+    submodules=None,
+    submod_attrs=None,
+    lazy_submodules=False,
+):
     """Attach lazily loaded submodules, functions, or other attributes.
 
     Typically, modules import submodules and attributes as follows::
@@ -50,6 +55,10 @@ def attach(package_name, submodules=None, submod_attrs=None):
     submod_attrs : dict
         Dictionary of submodule -> list of attributes / functions.
         These attributes are imported as they are used.
+    lazy_submodules : bool
+        Whether to lazily load submodules. If set to `True`, submodules are
+        returned as lazy proxies. Note that attribute access from
+        submod_attrs will trigger the import of the submodule.
 
     Returns
     -------
@@ -72,7 +81,11 @@ def attach(package_name, submodules=None, submod_attrs=None):
 
     def __getattr__(name):
         if name in submodules:
-            return importlib.import_module(f"{package_name}.{name}")
+            submod_path = f"{package_name}.{name}"
+            if lazy_submodules:
+                return load(submod_path, suppress_warning=True)
+            else:
+                return importlib.import_module(submod_path)
         elif name in attr_to_modules:
             submod_path = f"{package_name}.{attr_to_modules[name]}"
             submod = importlib.import_module(submod_path)
diff --git a/tests/test_lazy_loader.py b/tests/test_lazy_loader.py
index d68537f..419b1b0 100644
--- a/tests/test_lazy_loader.py
+++ b/tests/test_lazy_loader.py
@@ -86,7 +86,8 @@ def test_lazy_import_nonbuiltins():
             sp.pi
 
 
-def test_lazy_attach():
+@pytest.mark.parametrize("lazy_submodules", [False, True])
+def test_lazy_attach(lazy_submodules):
     name = "mymod"
     submods = ["mysubmodule", "anothersubmodule"]
     myall = {"not_real_submod": ["some_var_or_func"]}
@@ -96,8 +97,12 @@ def test_lazy_attach():
         "name": name,
         "submods": submods,
         "myall": myall,
+        "lazy_submods": lazy_submodules,
     }
-    s = "__getattr__, __lazy_dir__, __all__ = attach(name, submods, myall)"
+    s = (
+        "__getattr__, __lazy_dir__, __all__ = "
+        "attach(name, submods, myall, lazy_submodules=lazy_submods)"
+    )
 
     exec(s, {}, locls)
     expected = {
@@ -105,6 +110,7 @@ def test_lazy_attach():
         "name": name,
         "submods": submods,
         "myall": myall,
+        "lazy_submods": lazy_submodules,
         "__getattr__": None,
         "__lazy_dir__": None,
         "__all__": None,
@@ -135,9 +141,13 @@ def test_lazy_attach_noattrs():
     assert all_ == sorted(submods)
 
 
-def test_lazy_attach_returns_copies():
+@pytest.mark.parametrize("lazy_submodules", [False, True])
+def test_lazy_attach_returns_copies(lazy_submodules):
     _get, _dir, _all = lazy.attach(
-        __name__, ["my_submodule", "another_submodule"], {"foo": ["some_attr"]}
+        __name__,
+        ["my_submodule", "another_submodule"],
+        {"foo": ["some_attr"]},
+        lazy_submodules=lazy_submodules,
     )
     assert _dir() is not _dir()
     assert _dir() == _all