diff --git a/src/smolagents/local_python_executor.py b/src/smolagents/local_python_executor.py
index 5fe7401..86fa160 100644
--- a/src/smolagents/local_python_executor.py
+++ b/src/smolagents/local_python_executor.py
@@ -984,7 +984,8 @@ def get_safe_module(raw_module, dangerous_patterns, authorized_imports, visited=
     for attr_name in dir(raw_module):
         # Skip dangerous patterns at any level
         if any(
-            pattern in raw_module.__name__.split(".") + [attr_name] and pattern not in authorized_imports
+            pattern in raw_module.__name__.split(".") + [attr_name]
+            and not check_module_authorized(pattern, authorized_imports, dangerous_patterns)
             for pattern in dangerous_patterns
         ):
             logger.info(f"Skipping dangerous attribute {raw_module.__name__}.{attr_name}")
@@ -1007,6 +1008,18 @@ def get_safe_module(raw_module, dangerous_patterns, authorized_imports, visited=
     return safe_module
 
 
+def check_module_authorized(module_name, authorized_imports, dangerous_patterns):
+    if "*" in authorized_imports:
+        return True
+    else:
+        module_path = module_name.split(".")
+        if any([module in dangerous_patterns and module not in authorized_imports for module in module_path]):
+            return False
+        # ["A", "B", "C"] -> ["A", "A.B", "A.B.C"]
+        module_subpaths = [".".join(module_path[:i]) for i in range(1, len(module_path) + 1)]
+        return any(subpath in authorized_imports for subpath in module_subpaths)
+
+
 def import_modules(expression, state, authorized_imports):
     dangerous_patterns = (
         "_os",
@@ -1028,19 +1041,9 @@ def import_modules(expression, state, authorized_imports):
         "multiprocessing",
     )
 
-    def check_module_authorized(module_name):
-        if "*" in authorized_imports:
-            return True
-        else:
-            module_path = module_name.split(".")
-            if any([module in dangerous_patterns and module not in authorized_imports for module in module_path]):
-                return False
-            module_subpaths = [".".join(module_path[:i]) for i in range(1, len(module_path) + 1)]
-            return any(subpath in authorized_imports for subpath in module_subpaths)
-
     if isinstance(expression, ast.Import):
         for alias in expression.names:
-            if check_module_authorized(alias.name):
+            if check_module_authorized(alias.name, authorized_imports, dangerous_patterns):
                 raw_module = import_module(alias.name)
                 state[alias.asname or alias.name] = get_safe_module(raw_module, dangerous_patterns, authorized_imports)
             else:
@@ -1049,7 +1052,7 @@ def import_modules(expression, state, authorized_imports):
                 )
         return None
     elif isinstance(expression, ast.ImportFrom):
-        if check_module_authorized(expression.module):
+        if check_module_authorized(expression.module, authorized_imports, dangerous_patterns):
             raw_module = __import__(expression.module, fromlist=[alias.name for alias in expression.names])
             module = get_safe_module(raw_module, dangerous_patterns, authorized_imports)
             if expression.names[0].name == "*":  # Handle "from module import *"
diff --git a/tests/test_local_python_executor.py b/tests/test_local_python_executor.py
index cab9e10..ca1f8b0 100644
--- a/tests/test_local_python_executor.py
+++ b/tests/test_local_python_executor.py
@@ -25,6 +25,7 @@ from smolagents.default_tools import BASE_PYTHON_TOOLS
 from smolagents.local_python_executor import (
     InterpreterError,
     PrintContainer,
+    check_module_authorized,
     evaluate_delete,
     evaluate_python_code,
     fix_final_answer_code,
@@ -975,6 +976,10 @@ texec(tcompile("1 + 1", "no filename", "exec"))
         dangerous_code = "import os; os.listdir('./')"
         evaluate_python_code(dangerous_code, authorized_imports=["os"])
 
+    def test_can_import_os_if_all_imports_authorized(self):
+        dangerous_code = "import os; os.listdir('./')"
+        evaluate_python_code(dangerous_code, authorized_imports=["*"])
+
 
 @pytest.mark.parametrize(
     "code, expected_result",
@@ -1205,3 +1210,39 @@ class TestPrintContainer:
         pc = PrintContainer()
         pc.append("Hello")
         assert len(pc) == 5
+
+
+@pytest.mark.parametrize(
+    "module,authorized_imports,expected",
+    [
+        ("os", ["*"], True),
+        ("AnyModule", ["*"], True),
+        ("os", ["os"], True),
+        ("AnyModule", ["AnyModule"], True),
+        ("Module.os", ["Module"], False),
+        ("Module.os", ["Module", "os"], True),
+        ("os.path", ["os"], True),
+        ("os", ["os.path"], False),
+    ],
+)
+def test_check_module_authorized(module: str, authorized_imports: list[str], expected: bool):
+    dangerous_patterns = (
+        "_os",
+        "os",
+        "subprocess",
+        "_subprocess",
+        "pty",
+        "system",
+        "popen",
+        "spawn",
+        "shutil",
+        "sys",
+        "pathlib",
+        "io",
+        "socket",
+        "compile",
+        "eval",
+        "exec",
+        "multiprocessing",
+    )
+    assert check_module_authorized(module, authorized_imports, dangerous_patterns) == expected