Releaving Date Later Than Joining Date

Hi,
I have landed in an awkward situation and really don't know what to do..
I have resigned from current company and serving my 1 month notice period. There is about a week to go for my notice to get over. Meanwhile my future employer wants me to join them now itself so that they can file my B1. They dont want me to work for a week as i need the serve the notice period. This means my joining date in new company would be earlier than relieving date in the current company. Its a matter of 7 days but i don't want to take chances and so need advice from you guys

Kindly do Not take Risk,,,
Relieve from the current employer,,,,
Take Appointment Letter & Join the New Company,,,
It may lead to problems in future,,,,

Yes, the same situation has been faced by my organization that we have issued him joining letter and later the candidate find himself unable to submit him reliving letter before his present joining.
We have cancelled and taken back his joining letter and issue again it after submitting his reliving letter.
Ajay Singh