I deal almost exclusively with military tenants and I have done this several times, most before all the new online document services were available. I faxed an unsigned copy of the lease and they signed and sent back, they transferred funds electronically to my bank account ( I have a separate account for tenants so they don't have my "personal" numbers), as long as the funds go in, I sign and their place is ready when they get here. In the future I will make more use of the online stuff now that its available, like @Elizabeth Colegrove does. About every other tenant I get starts the renting process from across country, my main thing is that I am as honest as possible about the property and look of the neighborhood and have even emailed a video walk thru to them since photos can be deceiving size-wise and make a 1000 ft prop look like a 1700! It's in my best interest so I don't have issues later when they get here.