Client Certificate and IIS6 and "Choose a Digital Certificate"

Both client and server are the same machine (mine). I have created a server
and client certificates from internal microsoft certificate server.
Installed both of them into my machine into current user store. I also made
the CA to be trusted.

The web server is modified to use SSL with server certificate. This works
fine from the IE. Now I modified web server settings to require client
certificates. When I navigate to the secure page (that requires client
certificate), IE shows 'choose a digital certificate' dialog box and it has
no certificates in it. When I use Certicates mmc, I see the certificates in
'other people' store.

How do I solve this problem?

Thanks.
Raghu/..