Issue recreating project and/or organization

Is it possible to recreate an organization and/or project after they have been deleted?

Ive been experimenting with the APIs and i get this error when I try to re-create a project:

A project with identifier Foo and orgIdentifier default is already present or was deleted

I get a similar error when trying to recreate a previously deleted org.

Ive looked at the docs and I cant find anything expalining why/how I can do this.