diff --git a/pydantic_ai_slim/pydantic_ai/tools.py b/pydantic_ai_slim/pydantic_ai/tools.py
index 746a3ebc69..54f7a9affa 100644
--- a/pydantic_ai_slim/pydantic_ai/tools.py
+++ b/pydantic_ai_slim/pydantic_ai/tools.py
@@ -4,11 +4,11 @@
 import inspect
 from collections.abc import Awaitable
 from dataclasses import dataclass, field
-from typing import TYPE_CHECKING, Any, Callable, Generic, TypeVar, Union, cast
+from typing import TYPE_CHECKING, Any, Callable, Generic, Union, cast
 
 from pydantic import ValidationError
 from pydantic_core import SchemaValidator
-from typing_extensions import Concatenate, ParamSpec, TypeAlias
+from typing_extensions import Concatenate, ParamSpec, TypeAlias, TypeVar
 
 from . import _pydantic, _utils, messages as _messages, models
 from .exceptions import ModelRetry, UnexpectedModelBehavior
@@ -30,7 +30,7 @@
     'ToolDefinition',
 )
 
-AgentDeps = TypeVar('AgentDeps')
+AgentDeps = TypeVar('AgentDeps', default=None)
 """Type variable for agent dependencies."""
 
 
@@ -67,7 +67,7 @@ def replace_with(
         return dataclasses.replace(self, **kwargs)
 
 
-ToolParams = ParamSpec('ToolParams')
+ToolParams = ParamSpec('ToolParams', default=...)
 """Retrieval function param spec."""
 
 SystemPromptFunc = Union[
@@ -92,7 +92,7 @@ def replace_with(
 Usage `ToolPlainFunc[ToolParams]`.
 """
 ToolFuncEither = Union[ToolFuncContext[AgentDeps, ToolParams], ToolFuncPlain[ToolParams]]
-"""Either part_kind of tool function.
+"""Either kind of tool function.
 
 This is just a union of [`ToolFuncContext`][pydantic_ai.tools.ToolFuncContext] and
 [`ToolFuncPlain`][pydantic_ai.tools.ToolFuncPlain].
@@ -134,7 +134,7 @@ def hitchhiker(ctx: RunContext[int], answer: str) -> str:
 class Tool(Generic[AgentDeps]):
     """A tool function for an agent."""
 
-    function: ToolFuncEither[AgentDeps, ...]
+    function: ToolFuncEither[AgentDeps]
     takes_ctx: bool
     max_retries: int | None
     name: str
@@ -150,7 +150,7 @@ class Tool(Generic[AgentDeps]):
 
     def __init__(
         self,
-        function: ToolFuncEither[AgentDeps, ...],
+        function: ToolFuncEither[AgentDeps],
         *,
         takes_ctx: bool | None = None,
         max_retries: int | None = None,
diff --git a/tests/typed_agent.py b/tests/typed_agent.py
index 3871037716..040485af92 100644
--- a/tests/typed_agent.py
+++ b/tests/typed_agent.py
@@ -196,7 +196,8 @@ def foobar_plain(x: str, y: int) -> str:
 Tool(foobar_ctx, takes_ctx=True)
 Tool(foobar_ctx)
 Tool(foobar_plain, takes_ctx=False)
-Tool(foobar_plain)
+assert_type(Tool(foobar_plain), Tool[None])
+assert_type(Tool(foobar_plain), Tool)
 
 # unfortunately we can't type check these cases, since from a typing perspect `foobar_ctx` is valid as a plain tool
 Tool(foobar_ctx, takes_ctx=False)
@@ -206,12 +207,15 @@ def foobar_plain(x: str, y: int) -> str:
 Agent('test', tools=[foobar_plain], deps_type=int)
 Agent('test', tools=[foobar_plain])
 Agent('test', tools=[Tool(foobar_ctx)], deps_type=int)
-Agent('test', tools=[Tool(foobar_plain)], deps_type=int)
 Agent('test', tools=[Tool(foobar_ctx), foobar_ctx, foobar_plain], deps_type=int)
+Agent('test', tools=[Tool(foobar_ctx), foobar_ctx, Tool(foobar_plain)], deps_type=int)
 
 Agent('test', tools=[foobar_ctx], deps_type=str)  # pyright: ignore[reportArgumentType]
+Agent('test', tools=[Tool(foobar_ctx), Tool(foobar_plain)], deps_type=str)  # pyright: ignore[reportArgumentType]
 Agent('test', tools=[foobar_ctx])  # pyright: ignore[reportArgumentType]
 Agent('test', tools=[Tool(foobar_ctx)])  # pyright: ignore[reportArgumentType]
+# since deps are not set, they default to `None`, so can't be `int`
+Agent('test', tools=[Tool(foobar_plain)], deps_type=int)  # pyright: ignore[reportArgumentType]
 
 # prepare example from docs:
 
@@ -238,6 +242,7 @@ async def prepare_greet(ctx: RunContext[str], tool_def: ToolDefinition) -> ToolD
     default_agent = Agent()
     assert_type(default_agent, Agent[None, str])
     assert_type(default_agent, Agent[None])
+    assert_type(default_agent, Agent)
 
 partial_agent: Agent[MyDeps] = Agent(deps_type=MyDeps)
 assert_type(partial_agent, Agent[MyDeps, str])