Getting Fit: Training For a 10K Race

I've decided to register for a 10K race. In the past I've ran in four 5K races, but never 10K. Since I'm in okay-shape, I'll be able to finish the race without walking, but I'm certainly not going to be able to finish with a competitive time. My plan is (to do what I did with the 5k races) to get the best time I can in this race, and then try to beat that by a goal amount the next time. Last night I started doing a little interval training on the treadmill to help me prep for the race. My workout was:

5 minutes warm-up run at 7mph
10 minutes of 30sec/8.5 mph and 30sec/6.0mph
10 minutes of 30 sec/8.5mph and 60 sec/6.0mph
10 minutes run at 6.5mph
5 minutes cool-down walk at 3.8mph

Next time I'll try to extend these interval runs to more time. This 10K is going to be at the end of July (in about 7 weeks), so that should be enough time to make some good improvements on these intervals.