Coupon Code Single Use Issue

What I'm hoping to do: set up a single-use coupon for anyone, even those who are not yet users.

What I attempted: I thought applying the Per User LImit to "1" would take care of it.

What happens: This makes the coupon invalid for people who have not yet become users. Only removing the Per User Limit fixes it, but that opens the coupon up to multiple uses by the same user.

Any ideas how to make this work? Thanks in advance!