diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index a54fd8823..471870533 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -11,7 +11,6 @@
 from contextlib import asynccontextmanager
 from dataclasses import dataclass
 from datetime import timedelta
-from typing import Any
 
 import anyio
 import httpx
@@ -52,14 +51,10 @@
 class StreamableHTTPError(Exception):
     """Base exception for StreamableHTTP transport errors."""
 
-    pass
-
 
 class ResumptionError(StreamableHTTPError):
     """Raised when resumption request is invalid."""
 
-    pass
-
 
 @dataclass
 class RequestContext:
@@ -71,7 +66,7 @@ class RequestContext:
     session_message: SessionMessage
     metadata: ClientMessageMetadata | None
     read_stream_writer: StreamWriter
-    sse_read_timeout: timedelta
+    sse_read_timeout: float
 
 
 class StreamableHTTPTransport:
@@ -80,9 +75,9 @@ class StreamableHTTPTransport:
     def __init__(
         self,
         url: str,
-        headers: dict[str, Any] | None = None,
-        timeout: timedelta = timedelta(seconds=30),
-        sse_read_timeout: timedelta = timedelta(seconds=60 * 5),
+        headers: dict[str, str] | None = None,
+        timeout: float | timedelta = 30,
+        sse_read_timeout: float | timedelta = 60 * 5,
         auth: httpx.Auth | None = None,
     ) -> None:
         """Initialize the StreamableHTTP transport.
@@ -96,10 +91,12 @@ def __init__(
         """
         self.url = url
         self.headers = headers or {}
-        self.timeout = timeout
-        self.sse_read_timeout = sse_read_timeout
+        self.timeout = timeout.total_seconds() if isinstance(timeout, timedelta) else timeout
+        self.sse_read_timeout = (
+            sse_read_timeout.total_seconds() if isinstance(sse_read_timeout, timedelta) else sse_read_timeout
+        )
         self.auth = auth
-        self.session_id: str | None = None
+        self.session_id = None
         self.request_headers = {
             ACCEPT: f"{JSON}, {SSE}",
             CONTENT_TYPE: JSON,
@@ -160,7 +157,7 @@ async def _handle_sse_event(
                 return isinstance(message.root, JSONRPCResponse | JSONRPCError)
 
             except Exception as exc:
-                logger.error(f"Error parsing SSE message: {exc}")
+                logger.exception("Error parsing SSE message")
                 await read_stream_writer.send(exc)
                 return False
         else:
@@ -184,10 +181,7 @@ async def handle_get_stream(
                 "GET",
                 self.url,
                 headers=headers,
-                timeout=httpx.Timeout(
-                    self.timeout.total_seconds(),
-                    read=self.sse_read_timeout.total_seconds(),
-                ),
+                timeout=httpx.Timeout(self.timeout, read=self.sse_read_timeout),
             ) as event_source:
                 event_source.response.raise_for_status()
                 logger.debug("GET SSE connection established")
@@ -216,10 +210,7 @@ async def _handle_resumption_request(self, ctx: RequestContext) -> None:
             "GET",
             self.url,
             headers=headers,
-            timeout=httpx.Timeout(
-                self.timeout.total_seconds(),
-                read=ctx.sse_read_timeout.total_seconds(),
-            ),
+            timeout=httpx.Timeout(self.timeout, read=self.sse_read_timeout),
         ) as event_source:
             event_source.response.raise_for_status()
             logger.debug("Resumption GET SSE connection established")
@@ -412,9 +403,9 @@ def get_session_id(self) -> str | None:
 @asynccontextmanager
 async def streamablehttp_client(
     url: str,
-    headers: dict[str, Any] | None = None,
-    timeout: timedelta = timedelta(seconds=30),
-    sse_read_timeout: timedelta = timedelta(seconds=60 * 5),
+    headers: dict[str, str] | None = None,
+    timeout: float | timedelta = 30,
+    sse_read_timeout: float | timedelta = 60 * 5,
     terminate_on_close: bool = True,
     httpx_client_factory: McpHttpClientFactory = create_mcp_http_client,
     auth: httpx.Auth | None = None,
@@ -449,10 +440,7 @@ async def streamablehttp_client(
 
             async with httpx_client_factory(
                 headers=transport.request_headers,
-                timeout=httpx.Timeout(
-                    transport.timeout.total_seconds(),
-                    read=transport.sse_read_timeout.total_seconds(),
-                ),
+                timeout=httpx.Timeout(transport.timeout, read=transport.sse_read_timeout),
                 auth=transport.auth,
             ) as client:
                 # Define callbacks that need access to tg