A snippet of headers I get on login:
Set-Cookie: langpref=en_LJ/1107790991; path=/; domain=.livejournal.com
Set-Cookie: langpref=en_LJ/1107790991; path=/
Set-Cookie: BMLschemepref=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/; domain=.livejournal.com
Set-Cookie: BMLschemepref=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/
Set-Cookie: ljsession=ws:evan:[XXX]; path=/; domain=.livejournal.com; HttpOnly
Set-Cookie: ljsession=ws:evan:[XXX]; path=/; HttpOnly
Set-Cookie: betatest=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/; domain=.livejournal.com
Set-Cookie: betatest=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/
Set-Cookie: ljfastserver=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/; domain=.livejournal.com
Set-Cookie: ljfastserver=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/
Set-Cookie: langpref=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/; domain=.livejournal.com
Set-Cookie: langpref=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/
Set-Cookie: ljsession=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/; domain=.livejournal.com
Set-Cookie: ljsession=; expires=Thursday, 01-Jan-1970 00:00:00 GMT; path=/
As you can see, the login is set and cleared in one request.