When I applied for my current position (in 2008), I kept getting "thanks for playing, not interested" postcards from jurisdictions for positions I was easily qualified for. I then amended my resume cover letter, explaining that I would participate in the interview process and any pre-employment testing at my own expense. I also stated clearly that I was not seeking reimbursement for moving expenses, and that I had already arranged housing and could have a state driver's license within 30 days of being hired. Lastly, I explained that I was seeking to move because I had family in the area. The first resume that included my amended letter got me a job.
They started me with a written questionnaire (7 essay questions, one page responses). When I made the cut from that, they wanted a personal interview (oral boards). I flew myself out and participated. They offered me the position subject to a criminal background check, drug test and psychological evaluation (uh-oh), so I flew myself out again and got those things taken care of.
It wasn't cheap, but I knew the state of the economy would bring them several qualified candidates. If I wanted the job, I had to make it as convenient for them to interview me as it would have been for them to interview the guy living accross the street.