@@ -706,16 +706,11 @@ async def handler(args: dict[str, Any]) -> dict[str, Any]:
             except Exception as e:
                 return {"content": [{"type": "text", "text": f"Error: {e}"}]}
 
-        # Get JSON schema from the pydantic model or the JSON schema the tool was declared with
+        # Pass the full JSON schema through (from the pydantic model or the schema the tool was declared with), so
+        # keywords such as additionalProperties and $defs reach Claude. The SDK only uses a dict as a JSON schema when
+        # it has a string "type" and "properties", so both are always set.
         schema: dict[str, Any] = func_tool.parameters()
-        input_schema: dict[str, Any] = {
-            "type": "object",
-            "properties": schema.get("properties", {}),
-            "required": schema.get("required", []),
-        }
-        # Preserve $defs for nested type references (Pydantic uses $defs for nested models)
-        if "$defs" in schema:
-            input_schema["$defs"] = schema["$defs"]
+        input_schema: dict[str, Any] = {**schema, "type": "object", "properties": schema.get("properties") or {}}
 
         return SdkMcpTool(
             name=func_tool.name,
 
@@ -1,5 +1,6 @@
 # Copyright (c) Microsoft. All rights reserved.
 
+import copy
 import json
 from types import SimpleNamespace
 from typing import Any, cast
@@ -794,30 +795,87 @@ def create_person(person: Person) -> str:
         assert "person" in input_schema["properties"]
 
     async def test_function_tool_to_sdk_mcp_tool_uses_json_schema(self) -> None:
-        """Test that a tool declared with a JSON schema keeps its parameters."""
+        """Test that a tool declared with a JSON schema keeps the full schema, including additionalProperties."""
+        schema: dict[str, Any] = {
+            "type": "object",
+            "title": "WeatherInput",
+            "properties": {
+                "city": {"type": "string", "description": "City name"},
+                "unit": {"$ref": "#/$defs/Unit"},
+            },
+            "required": ["city"],
+            "additionalProperties": False,
+            "$defs": {"Unit": {"type": "string", "enum": ["celsius", "fahrenheit"]}},
+        }
 
-        @tool(
-            schema={
-                "type": "object",
-                "properties": {"city": {"type": "string", "description": "City name"}},
-                "required": ["city"],
-            }
-        )
-        def get_weather(city: str) -> str:
+        @tool(schema=schema)
+        def get_weather(city: str, unit: str = "celsius") -> str:
             """Get the weather."""
             return f"Sunny in {city}"
 
         agent = ClaudeAgent()
         sdk_tool = agent._function_tool_to_sdk_mcp_tool(get_weather)  # type: ignore[reportPrivateUsage]
 
-        assert sdk_tool.input_schema == {
-            "type": "object",
-            "properties": {"city": {"type": "string", "description": "City name"}},
-            "required": ["city"],
-        }
+        assert sdk_tool.input_schema == schema
+        assert cast(dict[str, Any], sdk_tool.input_schema)["additionalProperties"] is False
         result = await sdk_tool.handler({"city": "Paris"})
         assert result["content"][0]["text"] == "Sunny in Paris"
 
+    def test_function_tool_to_sdk_mcp_tool_keeps_input_model_keywords(self) -> None:
+        """Test that top-level keywords of a pydantic input model, such as additionalProperties, are kept."""
+        from pydantic import BaseModel, ConfigDict
+
+        class WeatherInput(BaseModel):
+            model_config = ConfigDict(extra="forbid")
+            city: str
+
+        @tool(schema=WeatherInput)
+        def get_weather(city: str) -> str:
+            """Get the weather."""
+            return f"Sunny in {city}"
+
+        agent = ClaudeAgent()
+        sdk_tool = agent._function_tool_to_sdk_mcp_tool(get_weather)  # type: ignore[reportPrivateUsage]
+
+        assert sdk_tool.input_schema == WeatherInput.model_json_schema()
+        assert cast(dict[str, Any], sdk_tool.input_schema)["additionalProperties"] is False
+
+    @pytest.mark.parametrize(
+        ("schema", "expected"),
+        [
+            (
+                {"properties": {"city": {"type": "string"}}},
+                {"type": "object", "properties": {"city": {"type": "string"}}},
+            ),
+            (
+                {"type": "object", "additionalProperties": False},
+                {"type": "object", "properties": {}, "additionalProperties": False},
+            ),
+            (
+                {"type": ["object", "null"], "properties": {"city": {"type": "string"}}},
+                {"type": "object", "properties": {"city": {"type": "string"}}},
+            ),
+            ({"type": "object", "properties": None}, {"type": "object", "properties": {}}),
+            ({}, {"type": "object", "properties": {}}),
+        ],
+        ids=["no-type", "no-properties", "list-type", "null-properties", "empty"],
+    )
+    def test_function_tool_to_sdk_mcp_tool_sets_type_and_properties(
+        self, schema: dict[str, Any], expected: dict[str, Any]
+    ) -> None:
+        """Test that a schema without an object type or properties still reaches the SDK as a JSON schema."""
+        declared = copy.deepcopy(schema)
+
+        @tool(name="lookup", description="Look something up.", schema=schema)
+        def lookup(**kwargs: Any) -> str:
+            return "ok"
+
+        agent = ClaudeAgent()
+        sdk_tool = agent._function_tool_to_sdk_mcp_tool(lookup)  # type: ignore[reportPrivateUsage]
+
+        assert sdk_tool.input_schema == expected
+        assert lookup.parameters() == declared
+
     async def test_tool_handler_success(self) -> None:
         """Test tool handler executes successfully."""