Killing Kookies

[ClevrMnkey]

I am having a devil of a time getting rid of cookies. Because of the
silly 20 cookies/domain limit of IE I need to clear them out when
vistors go from one area through a portal to the next.

Here is the script I am working with:

if (Request.Cookies.Count 0)
{
// Remove all domain cookies
Response.Cookies.Clear();
System.Web.HttpCookie ck;
int cookiejar = Request.Cookies.Count; // This does not
work within the for() statement
for (int i = 0; i < cookiejar; i++)
{
ck = Request.Cookies[i];
ck.Value = null;
ck.Path = "/";
ck.Expires = System.DateTime.Now.AddYears(-1);
Response.Cookies.Add(ck);
}
}
Response.Redirect("someotherurl");

This didn't work, so I tried again with a 200 response instead of a
302.
Here's what it looks like from Fiddler

GET /url.aspx HTTP/1.1
Accept: */*
Accept-Language: en-us
UA-CPU: x86
Accept-Encoding: gzip, deflate
User-Agent: Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 5.1; .NET
CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1; .NET CLR 3.0.04506.30)
Host: mydomain.com
Proxy-Connection: Keep-Alive
Pragma: no-cache
Cookie: searchprefs=somevalue; usersessionid=someguid;
supplierid=someint

And the response is:

HTTP/1.1 200 OK
Via: 1.1 CEREBUS
Connection: Keep-Alive
Proxy-Connection: Keep-Alive
Content-Length: 34
Date: Thu, 22 Mar 2007 14:21:23 GMT
Content-Type: text/html; charset=utf-8
Server: Microsoft-IIS/6.0
Cache-Control: private
X-AspNet-Version: 2.0.50727
Set-Cookie: searchprefs=; expires=Wed, 22-Mar-2006 14:21:23 GMT;
path=/
Set-Cookie: usersessionid=; expires=Wed, 22-Mar-2006 14:21:23 GMT;
path=/
Set-Cookie: supplierid=; expires=Wed, 22-Mar-2006 14:21:23 GMT; path=/

This looks good to me, but the browser does not discard the cookies.
Any ideas?