Accessing mixed authentication web app with Client Object Model and Web Serices

I have mixed authentication web app in SharePoint 2010: both Windows (NTLM) and Forms based.
When I tried to access it using Client Object Model with my NTLM credentials I got 401 (Unauthorized) exception. I googled and found this solution

...
clientContext.ExecutingWebRequest += new EventHandler(clientContext_ExecutingWebRequest);
...
}

static void clientContext_ExecutingWebRequest(object sender, WebRequestEventArgs e)
{
e.WebRequestExecutor.WebRequest.Headers.Add("X-FORMS_BASED_AUTH_ACCEPTED", "f");
}


This works well for me.

Then when I tried to access same site using Lists.asmx web service with same NTLM credentials I got exactly same exception.
I added this method to the Web Service wrapper class (it's in Web References > ListWebService > Reference.map > Reference.cs in my case)


protected override System.Net.WebRequest GetWebRequest(Uri uri)
{
System.Net.WebRequest wr = base.GetWebRequest(uri);
wr.Headers.Add("X-FORMS_BASED_AUTH_ACCEPTED", "f");
return wr;
}

That solved the issue as well.