When I had to ran the mile (like 5 years ago, jesus it's been a long time) the most effective strategy for me was to sprint the first lap or two (if I could) and then jog the rest. I found that regardless of whether or not I sprinted the first lap I'd take the remaining laps at about the same speed, so sprinting the first lap cut out all that extra time I spent on the first lap. Also, instead of pushing myself the whole time, I only pushed myself during the first lap so by the time I got to the third or fourth I felt somewhat replenished and could speed it up again.