diff --git a/src/agents/tool.py b/src/agents/tool.py
index 0baf2c0c..3c309217 100644
--- a/src/agents/tool.py
+++ b/src/agents/tool.py
@@ -190,8 +190,11 @@ def function_tool(
         failure_error_function: If provided, use this function to generate an error message when
             the tool call fails. The error message is sent to the LLM. If you pass None, then no
             error message will be sent and instead an Exception will be raised.
-        strict_mode: If False, parameters with default values become optional in the
-            function schema.
+        strict_mode: Whether to enable strict mode for the tool's JSON schema. We *strongly*
+            recommend setting this to True, as it increases the likelihood of correct JSON input.
+            If False, it allows non-strict JSON schemas. For example, if a parameter has a default
+            value, it will be optional, additional properties are allowed, etc. See here for more:
+            https://platform.openai.com/docs/guides/structured-outputs?api-mode=responses#supported-schemas
     """
 
     def _create_function_tool(the_func: ToolFunction[...]) -> FunctionTool:
diff --git a/tests/test_function_tool_decorator.py b/tests/test_function_tool_decorator.py
index f146ec7f..903dd123 100644
--- a/tests/test_function_tool_decorator.py
+++ b/tests/test_function_tool_decorator.py
@@ -152,9 +152,13 @@ def optional_param_function(a: int, b: Optional[int] = None) -> str:
 
 
 @pytest.mark.asyncio
-async def test_optional_param_function():
+async def test_non_strict_mode_function():
     tool = optional_param_function
 
+    assert tool.strict_json_schema is False, "strict_json_schema should be False"
+
+    assert tool.params_json_schema.get("required") == ["a"], "required should only be a"
+
     input_data = {"a": 5}
     output = await tool.on_invoke_tool(ctx_wrapper(), json.dumps(input_data))
     assert output == "5_no_b"
@@ -165,7 +169,7 @@ async def test_optional_param_function():
 
 
 @function_tool(strict_mode=False)
-def multiple_optional_params_function(
+def all_optional_params_function(
     x: int = 42,
     y: str = "hello",
     z: Optional[int] = None,
@@ -176,8 +180,12 @@ def multiple_optional_params_function(
 
 
 @pytest.mark.asyncio
-async def test_multiple_optional_params_function():
-    tool = multiple_optional_params_function
+async def test_all_optional_params_function():
+    tool = all_optional_params_function
+
+    assert tool.strict_json_schema is False, "strict_json_schema should be False"
+
+    assert tool.params_json_schema.get("required") is None, "required should be empty"
 
     input_data: dict[str, Any] = {}
     output = await tool.on_invoke_tool(ctx_wrapper(), json.dumps(input_data))