How to set cookie for other domain

Hi,

I am trying to set a cookie for another domain from my own server via serve=
rside Java/Servlet.
The other domain is not under my control. Is this possible with an appropri=
ate P3P policy stored on my own server?

I have already created a p3p.xml using IBMs policy editor, stored it on the=
 server and written a corresponding Compact Policy in the response header:

P3P: policyref=3D"http://localhost:8080/SSOProxyNew/w3c/p3p.xml", CP=3D"NOI=
 CURa ADMa DEVa TAIa OUR BUS IND UNI COM NAV INT"
Set-Cookie: mycookie=3DXXXXXX; Domain=3D.otherdomain.com; Expires=3DWed, 29=
-Oct-2008 13:17:06 GMT

But the browser (IE6 and IE7) does not seem to accept the cookie. At least =
the cookie does not show up in the request-headers to www.otherdomain.com a=
nd it is not listed in the browsers cookie-list.
There is no cookie-warning in the status-bar of the browser either.
Privacy Level is set to Medium in IE.

What am I doing wrong?
Is it generally possible to set cookies for other domains? I have seen ebay=
..com setting cookies for lots of other domains.

Thx
Mathias